Among the many knowledge that is a sign of literacy, the alphabet comes first. The next, equally “sign” element is the skills of addition-multiplication and, adjacent to them, but opposite in meaning, arithmetic operations of subtraction-division. The skills learned in distant school childhood serve faithfully day and night: TV, newspaper, SMS, and everywhere we read, write, count, add, subtract, multiply. And, tell me, have you often had to extract roots in your life, except at the dacha? For example, such an entertaining problem, like the square root of the number 12345... Is there still gunpowder in the flasks? Can we handle it? Nothing could be simpler! Where is my calculator... And without it, hand-to-hand combat is weak?

First, let's clarify what it is - the square root of a number. Generally speaking, “taking the root of a number” means performing the arithmetic operation opposite to raising to a power - here you have the unity of opposites in life application. Let's say a square is the multiplication of a number by itself, i.e., as taught at school, X * X = A or in another notation X2 = A, and in words - “X squared equals A.” Then the inverse problem sounds like this: the square root of the number A is the number X, which, when squared, equals A.

Taking the square root

From school course Arithmetic knows methods of calculations “in a column”, which help to perform any calculations using the first four arithmetic operations. Alas... For square, and not only square, roots, such algorithms do not exist. And in this case, how to extract the square root without a calculator? Based on the definition square root There is only one conclusion - it is necessary to select the value of the result by sequentially enumerating numbers whose square approaches the value of the radical expression. That's all! Before an hour or two has passed, you can calculate, using the well-known method of multiplication in a “column”, any square root. If you have the skills, this will only take a couple of minutes. Even a not-so-advanced user of a calculator or PC can do this in one fell swoop - progress.

But seriously, the calculation of the square root is often performed using the “artillery fork” technique: first take a number whose square approximately corresponds to the radical expression. It is better if “our square” is slightly smaller than this expression. Then they adjust the number according to their own skill and understanding, for example, multiply by two, and... square it again. If the result more number under the root, successively adjusting the original number, gradually approaching its “colleague” under the root. As you can see - no calculator, only the ability to count “in a column”. Of course, there are many scientifically proven and optimized algorithms for calculating the square root, but for “home use” the above technique gives 100% confidence in the result.

Yes, I almost forgot, to confirm our increased literacy, let’s calculate the square root of the previously indicated number 12345. We do it step by step:

1. Let's take, purely intuitively, X=100. Let's calculate: X * X = 10000. Intuition is at its best - the result is less than 12345.

2. Let’s try, also purely intuitively, X = 120. Then: X * X = 14400. And again, intuition is in order - the result is more than 12345.

3. Above we got a “fork” of 100 and 120. Let’s choose new numbers - 110 and 115. We get, respectively, 12100 and 13225 - the fork narrows.

4. Let’s try “maybe” X=111. We get X * X = 12321. This number is already quite close to 12345. In accordance with the required accuracy, the “fit” can be continued or stopped at the result obtained. That's it. As promised - everything is very simple and without a calculator.

Just a little history...

Thought of using it square roots also Pythagoreans, students of the school and followers of Pythagoras, 800 BC. and then we “ran into” new discoveries in the field of numbers. And where did that come from?

1. Solving the problem with extracting the root gives the result in the form of numbers of a new class. They were called irrational, in other words, “unreasonable”, because. they are not written as a complete number. The most classic example of this kind is the square root of 2. This case corresponds to calculating the diagonal of a square with a side equal to 1 - this is the influence of the Pythagorean school. It turned out that in a triangle with a very specific unit size of sides, the hypotenuse has a size that is expressed by a number that “has no end.” This is how they appeared in mathematics

2. It is known that it turned out that this mathematical operation contains another catch - when extracting the root, we do not know which number, positive or negative, is the square of the radical expression. This uncertainty, the double result from one operation, is recorded in this way.

The study of problems related to this phenomenon has become a direction in mathematics called the theory of complex variables, which has a large practical significance in mathematical physics.

It is curious that the same omnipresent I. Newton used the designation of the root - radical - in his “Universal Arithmetic”, and exactly modern look notation of the root has been known since 1690 from the book of the Frenchman Rolle “Manual of Algebra”.

    Well, if we take into account that this very square root is the product of the same number (that is, b = a), then the square root of one hundred will be 10 (100 = 10).

    It should be noted that the number 100 can be represented as the product of 25 and 4. And then calculate the square root of both 25 and 4. 5 and 2. Multiply and also get 10.

    When we first started studying this topic at school, square root of 100 was probably one of the easiest to understand and calculations. Usually I looked at an even (!) number of zeros and immediately calculated which number, multiplied by itself, gives the figure under the square root. For example, if it were 10000, then the square root of that number would be one hundred (100x100 = 10000). If the number under sq. the root is six zeros, then the answer will contain three zeros. Etc.

    In this case, there are only two zeros in the number, which means that there were two tens. So, The square root of 100 is 10. We check: 10x10 = 100

    There are several ways to calculate the square root.

    1) Take a calculator or smartphone/tablet/computer with a calculation program installed, enter the number 100 and click on the square root icon, which looks something like this:

    2) Know the table of squares of numbers up to 100=25*4.

    3) By division method.

    4) By the method of decomposition into prime factors 100=10*10.

    Theoretically, if you do everything correctly, you will get a result of 10.

    The icon used to represent a square root is called a radical and looks like this.

    And the square root of 100 is easy to extract if you know the squares of numbers. 10 X 10 = 100. So the square root of 100, following the definition of a square root, is 10.

    Probably every schoolchild knows that the number 100 is the product of 10 by 10.

    Since the square root is a number that, when multiplied by itself, is a radical expression, then The square root of one hundred is equal to the number 10.

    If you forgot that 100=10*10, then you can use the properties of roots:

    root of 100 = root of (25*4) = root of 25 * root of 4.

    Everyone knows that 5*5 = 25, and 2*2 = 4. Therefore, the root of 100 = 5 * 2 = 10.

    Well, if you don’t know this, then you can use a calculator or Excel tables, they have a special formula called ROOT. Here's how it all looks visually:

    Nowadays, using a calculator it is very easy to calculate the square root of any number.

    You can extract the square root of 100 orally. After all, it is known that bringing the number x to the square is the number x multiplied by the number x.

    If 10 10 = 100, then the square root of 100 is 10.

    Answer to the question: 10 .

    The square root in mathematics is denoted by a conventional symbol.

    The square root of a number is a non-negative number whose square is equal to a. Since 10^2=100, the square root of 100 is 10.

    There are numbers whose roots are very easy to remember. For me, this is, for example, 25 - the root will be 5, since 5*5=25, 625 is the root of 25, since 25*25=625.

    I also include the number 100 as such numbers - the root will be 10, check 10*10=100. So it's correct.

    Square root of one hundred? looks like it will be 10

    It’s hard to imagine that a person will go online to find this answer, but if we imagine that he is completely disorganized and inattentive, then I give the answer. The square root of the number 100 is 10, and also -10. Many sources write it this way.

    The square root of 100 has two values: 10 and -10. Those who don’t believe can check by multiplying.

    To extract the square root without a calculator, you need to resort to decomposing the number under the root into the smallest factors and proceed from there. So for the number one hundred:

    And accordingly, from here it immediately becomes clear that the square root of one hundred will be exactly 10.

    I had to remember a rule that I remembered from school:

    Although extracting the root of 100 is a simple matter that does not require the use of calculators, since it is ingrained in memory for life. The number 100 is obtained by multiplying 10 by 10, and therefore the number 10 and will be the root of a hundred.

Today we will figure out on this page of our website what the square root of 100 is. Let's figure out together what the square root of 100 is, since 1000 scientists have been racking their brains on this topic for many decades, and many have come to the inevitable conclusion from calculations that such a root does not exist at all and it is simply impossible to calculate it. It is also very important in this case to specify exactly correct question to identify the square root of 100. To be precise, we will calculate the arithmetic square root of 100, since in the ordinary square root of 100 we will end up with two numbers: 10 and -10.

We can calculate the sum of these numbers we need using a simple arithmetic technique using a vertical, familiar line, numbers and roots that are written in the lower right. There we will find the square of units of the root we need, then multiply the tens and find the double and not triple the product of the ten of any root by units. We will have to square some numbers so that the total becomes a two-digit number; if in the end we get the number 10, then we have done everything right with you. The main thing is to initially become at least a little familiar with mathematics and the mathematical progression of composing the square root before starting calculations.

Remember one single and basic rule: in order to extract the necessary square root from any integer, first of all we extract any root we need from the number of its sums and hundreds. If the number is equal to or greater than 100, then we begin to look for the root of the hundreds of actual numbers of these hundreds, then of the tens of thousands of the actual number, especially if the given number is much more than 100, then we necessarily extract the root of the number of hundreds of tens of thousands or to be more precise: out of a million of a given number. There are many rules and various scientific recommendations on this topic, school programs when extracting the square root of 100 will always be the same.

If we consider the progress of finding the root of the number 100, we need to pay attention to the fact that there are as many numbers in the root as there are under it. finite number sides, while the left side can consist of only one digit. Based on all this, the most accurate square root of any number on planet earth will be the sum of numbers whose square exactly when calculated is equal to given number. This is where we can end our short course by calculating the square root of 100 which will equal (10) ten.

Konstantinova Vera

How to find the root of a number

The problem of finding a root in mathematics is the inverse problem of raising a number to a power. There are different roots: roots of the second degree, roots of the third degree, roots of the fourth degree and so on. It depends on what power the number was originally raised to. The root is denoted by the symbol: √ is a square root, that is, the root of the second degree; if the root has a degree greater than the second, then the corresponding degree is assigned above the root sign. The number that is under the root sign is a radical expression. When finding the root, there are several rules that will help you not make a mistake in finding the root:

  • Even power root (if the power is 2, 4, 6, 8, etc.) of negative number Does NOT exist. If the radical expression is negative, but the root of an odd degree is sought (3, 5, 7, and so on), then the result will be negative.
  • The root of any power of one is always one: √1 = 1.
  • The root of zero is zero: √0 = 0.

How to find the root of 100

If the problem does not say what root of the degree needs to be found, then it usually means that it is necessary to find the root of the second degree (square).
Let's find √100 = ? We need to find a number that, when raised to the second power, gives the number 100. Obviously, such a number is the number 10, since: 10 2 = 100. Therefore, √100 = 10: the square root of 100 is 10.

When deciding various tasks In mathematics and physics courses, pupils and students are often faced with the need to extract roots of the second, third or nth degree. Of course, in the century information technology It won’t be difficult to solve this problem using a calculator. However, situations arise when it is impossible to use the electronic assistant.

For example, many exams do not allow you to bring electronics. In addition, you may not have a calculator at hand. In such cases, it is useful to know at least some methods for calculating radicals manually.

Finding square roots using a table of squares

One of the simplest ways to calculate roots is to using a special table. What is it and how to use it correctly?

Using the table, you can find the square of any number from 10 to 99. The rows of the table contain the values ​​of tens, and the columns contain the values ​​of units. The cell at the intersection of a row and a column contains a square double digit number. In order to calculate the square of 63, you need to find a row with a value of 6 and a column with a value of 3. At the intersection we will find a cell with the number 3969.

Since extracting the root is the inverse operation of squaring, to perform this action you must do the opposite: first find the cell with the number whose radical you want to calculate, then use the values ​​of the column and row to determine the answer. As an example, consider calculating the square root of 169.

We find a cell with this number in the table, horizontally we determine tens - 1, vertically we find units - 3. Answer: √169 = 13.

Similarly, you can calculate cube and nth roots using the appropriate tables.

The advantage of the method is its simplicity and the absence of additional calculations. The disadvantages are obvious: the method can only be used for a limited range of numbers (the number for which the root is found must be in the range from 100 to 9801). In addition, it will not work if the given number is not in the table.

Prime factorization

If the table of squares is not at hand or it turned out to be impossible to find the root with its help, you can try factor the number under the root into prime factors. Prime factors are those that can be completely (without remainder) divisible only by themselves or by one. Examples could be 2, 3, 5, 7, 11, 13, etc.

Let's look at calculating the root using √576 as an example. Let's break it down into prime factors. We get the following result: √576 = √(2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 ​​∙ 3) = √(2 ∙ 2 ∙ 2)² ∙ √3². Using the basic property of roots √a² = a, we will get rid of roots and squares, and then calculate the answer: 2 ∙ 2 ∙ 2 ∙ 3 ​​= 24.

What to do if any of the multipliers does not have its own pair? For example, consider the calculation of √54. After factorization, we obtain the result in the following form: √54 = √(2 ∙ 3 ​​∙ 3 ∙ 3) = √3² ∙ √(2 ∙ 3) = 3√6. The non-removable part can be left under the root. For most geometry and algebra problems, this will count as the final answer. But if there is a need to calculate approximate values, you can use methods that will be discussed below.

Heron's method

What to do when you need to at least approximately know what the extracted root is equal to (if it is impossible to obtain an integer value)? A quick and fairly accurate result is obtained by using the Heron method. Its essence is to use an approximate formula:

√R = √a + (R - a) / 2√a,

where R is the number whose root needs to be calculated, a is the nearest number whose root value is known.

Let's look at how the method works in practice and evaluate how accurate it is. Let's calculate what √111 is equal to. The number closest to 111, the root of which is known, is 121. Thus, R = 111, a = 121. Substitute the values ​​into the formula:

√111 = √121 + (111 - 121) / 2 ∙ √121 = 11 - 10 / 22 ≈ 10,55.

Now let's check the accuracy of the method:

10.55² = 111.3025.

The error of the method was approximately 0.3. If the accuracy of the method needs to be improved, you can repeat the previously described steps:

√111 = √111,3025 + (111 - 111,3025) / 2 ∙ √111,3025 = 10,55 - 0,3025 / 21,1 ≈ 10,536.

Let's check the accuracy of the calculation:

10.536² = 111.0073.

After re-applying the formula, the error became completely insignificant.

Calculating the root by long division

This method of finding the square root value is a little more complex than the previous ones. However, it is the most accurate among other calculation methods without a calculator.

Let's say that you need to find the square root accurate to 4 decimal places. Let's analyze the calculation algorithm using the example of an arbitrary number 1308.1912.

  1. Divide the sheet of paper into 2 parts with a vertical line, and then draw another line from it to the right, slightly below the top edge. Let's write the number on the left side, dividing it into groups of 2 digits, moving to the right and left of the decimal point. The very first digit on the left may be without a pair. If the sign is missing on the right side of the number, then you should add 0. In our case, the result will be 13 08.19 12.
  2. Let's choose the best large number, the square of which will be less than or equal to the first group of digits. In our case it is 3. Let's write it on the top right; 3 is the first digit of the result. On the bottom right we indicate 3×3 = 9; this will be needed for subsequent calculations. From 13 in the column we subtract 9, we get a remainder of 4.
  3. Let's assign the next pair of numbers to remainder 4; we get 408.
  4. Multiply the number at the top right by 2 and write it down at the bottom right, adding _ x _ = to it. We get 6_ x _ =.
  5. Instead of dashes, you need to substitute the same number, less than or equal to 408. We get 66 × 6 = 396. We write 6 from the top right, since this is the second digit of the result. Subtract 396 from 408, we get 12.
  6. Let's repeat steps 3-6. Since the digits moved down are in the fractional part of the number, it is necessary to place a decimal point at the top right after 6. Let's write down the double result with dashes: 72_ x _ =. A suitable number would be 1: 721×1 = 721. Let's write it down as the answer. Let's subtract 1219 - 721 = 498.
  7. Let's perform the sequence of actions given in the previous paragraph three more times to get the required number of decimal places. If there are not enough characters for further calculations, you need to add two zeros to the current number on the left.

As a result, we get the answer: √1308.1912 ≈ 36.1689. If you check the action using a calculator, you can make sure that all signs were identified correctly.

Bitwise square root calculation

The method is highly accurate. In addition, it is quite understandable and does not require memorizing formulas or a complex algorithm of actions, since the essence of the method is to select the correct result.

Let's extract the root of the number 781. Let's look at the sequence of actions in detail.

  1. Let's find out which digit of the square root value will be the most significant. To do this, let's square 0, 10, 100, 1000, etc. and find out between which of them the radical number is located. We get that 10²< 781 < 100², т. е. старшим разрядом будут десятки.
  2. Let's choose the value of tens. To do this, we will take turns raising to the power of 10, 20, ..., 90 until we get a number greater than 781. For our case, we get 10² = 100, 20² = 400, 30² = 900. The value of the result n will be within 20< n <30.
  3. Similar to the previous step, the value of the units digit is selected. Let's square 21.22, ..., 29 one by one: 21² = 441, 22² = 484, 23² = 529, 24² = 576, 25² = 625, 26² = 676, 27² = 729, 28² = 784. We get that 27< n < 28.
  4. Each subsequent digit (tenths, hundredths, etc.) is calculated in the same way as shown above. Calculations are carried out until the required accuracy is achieved.

Video

This video will show you how to find square roots without using a calculator.

Before calculators, students and teachers calculated square roots by hand. There are several ways to calculate the square root of a number manually. Some of them offer only an approximate solution, others give an exact answer.

Steps

Prime factorization

    Factor the radical number into factors that are square numbers. Depending on the radical number, you will get an approximate or exact answer. Square numbers are numbers from which the whole square root can be taken. Factors are numbers that, when multiplied, give the original number. For example, the factors of the number 8 are 2 and 4, since 2 x 4 = 8, the numbers 25, 36, 49 are square numbers, since √25 = 5, √36 = 6, √49 = 7. Square factors are factors , which are square numbers. First, try to factor the radical number into square factors.

    • For example, calculate the square root of 400 (by hand). First try factoring 400 into square factors. 400 is a multiple of 100, that is, divisible by 25 - this is a square number. Dividing 400 by 25 gives you 16. The number 16 is also a square number. Thus, 400 can be factored into the square factors of 25 and 16, that is, 25 x 16 = 400.
    • This can be written as follows: √400 = √(25 x 16).

  1. The square root of the product of some terms is equal to the product of the square roots of each term, that is, √(a x b) = √a x √b. Use this rule to take the square root of each square factor and multiply the results to find the answer.

    • In our example, take the root of 25 and 16.
      • √(25 x 16)
      • √25 x √16
      • 5 x 4 = 20

  2. If the radical number does not factor into two square factors (and this happens in most cases), you will not be able to find the exact answer in the form of a whole number. But you can simplify the problem by decomposing the radical number into a square factor and an ordinary factor (a number from which the whole square root cannot be taken). Then you will take the square root of the square factor and will take the root of the common factor.

    • For example, calculate the square root of the number 147. The number 147 cannot be factored into two square factors, but it can be factorized into the following factors: 49 and 3. Solve the problem as follows:
      • = √(49 x 3)
      • = √49 x √3
      • = 7√3

  3. If necessary, estimate the value of the root. Now you can estimate the value of the root (find an approximate value) by comparing it with the values ​​of the roots of the square numbers that are closest (on both sides of the number line) to the radical number. You will receive the root value as a decimal fraction, which must be multiplied by the number behind the root sign.

    • Let's return to our example. The radical number is 3. The square numbers closest to it will be the numbers 1 (√1 = 1) and 4 (√4 = 2). Thus, the value of √3 is located between 1 and 2. Since the value of √3 is probably closer to 2 than to 1, our estimate is: √3 = 1.7. We multiply this value by the number at the root sign: 7 x 1.7 = 11.9. If you do the math on a calculator, you'll get 12.13, which is pretty close to our answer.
      • This method also works with large numbers. For example, consider √35. The radical number is 35. The closest square numbers to it will be the numbers 25 (√25 = 5) and 36 (√36 = 6). Thus, the value of √35 is located between 5 and 6. Since the value of √35 is much closer to 6 than to 5 (because 35 is only 1 less than 36), we can say that √35 is slightly less than 6. Check on the calculator gives us the answer 5.92 - we were right.

  4. Another way - factor the radical number into prime factors . Prime factors are numbers that are divisible only by 1 and themselves. Write the prime factors in a series and find pairs of identical factors. Such factors can be taken out of the root sign.

    • For example, calculate the square root of 45. We factor the radical number into prime factors: 45 = 9 x 5, and 9 = 3 x 3. Thus, √45 = √(3 x 3 x 5). 3 can be taken out as a root sign: √45 = 3√5. Now we can estimate √5.
    • Let's look at another example: √88.
      • = √(2 x 44)
      • = √ (2 x 4 x 11)
      • = √ (2 x 2 x 2 x 11). You received three multipliers of 2; take a couple of them and move them beyond the root sign.
      • = 2√(2 x 11) = 2√2 x √11. Now you can evaluate √2 and √11 and find an approximate answer.

    Calculating square root manually

    Using long division

    1. This method involves a process similar to long division and gives an accurate answer. First, draw a vertical line dividing the sheet into two halves, and then to the right and slightly below the top edge of the sheet, draw a horizontal line to the vertical line. Now divide the radical number into pairs of numbers, starting with the fractional part after the decimal point. So, the number 79520789182.47897 is written as "7 95 20 78 91 82, 47 89 70".

      • For example, let's calculate the square root of the number 780.14. Draw two lines (as shown in the picture) and write the given number in the form “7 80, 14” at the top left. It is normal that the first digit from the left is an unpaired digit. You will write the answer (the root of this number) at the top right.

    2. For the first pair of numbers (or single number) from the left, find the largest integer n whose square is less than or equal to the pair of numbers (or single number) in question. In other words, find the square number that is closest to, but smaller than, the first pair of numbers (or single number) from the left, and take the square root of that square number; you will get the number n. Write the n you found at the top right, and write the square of n at the bottom right.

      • In our case, the first number on the left will be 7. Next, 4< 7, то есть 2 2 < 7 и n = 2. Напишите 2 сверху справа - это первая цифра в искомом квадратном корне. Напишите 2×2=4 справа снизу; вам понадобится это число для последующих вычислений.

    3. Subtract the square of the number n you just found from the first pair of numbers (or single number) on the left. Write the result of the calculation under the subtrahend (the square of the number n).

      • In our example, subtract 4 from 7 and get 3.

    4. Take down the second pair of numbers and write it down next to the value obtained in the previous step. Then double the number at the top right and write the result at the bottom right with the addition of "_×_=".

      • In our example, the second pair of numbers is "80". Write "80" after the 3. Then, double the number on the top right gives 4. Write "4_×_=" on the bottom right.

    5. Fill in the blanks on the right.

      • In our case, if we put the number 8 instead of dashes, then 48 x 8 = 384, which is more than 380. Therefore, 8 is too large a number, but 7 will do. Write 7 instead of dashes and get: 47 x 7 = 329. Write 7 at the top right - this is the second digit in the desired square root of the number 780.14.

    6. Subtract the resulting number from the current number on the left. Write the result from the previous step under the current number on the left, find the difference and write it under the subtrahend.

      • In our example, subtract 329 from 380, which equals 51.

    7. Repeat step 4. If the pair of numbers being transferred is the fractional part of the original number, then put a separator (comma) between the integer and fractional parts in the required square root at the top right. On the left, bring down the next pair of numbers. Double the number at the top right and write the result at the bottom right with the addition of "_×_=".

      • In our example, the next pair of numbers to be removed will be the fractional part of the number 780.14, so place the separator of the integer and fractional parts in the desired square root in the upper right. Take down 14 and write it down at the bottom left. Double the number on the top right (27) is 54, so write "54_×_=" on the bottom right.

    8. Repeat steps 5 and 6. Find the largest number in place of the dashes on the right (instead of the dashes you need to substitute the same number) so that the result of the multiplication is less than or equal to the current number on the left.

      • In our example, 549 x 9 = 4941, which is less than the current number on the left (5114). Write 9 on the top right and subtract the result of the multiplication from the current number on the left: 5114 - 4941 = 173.

    9. If you need to find more decimal places for the square root, write a couple of zeros to the left of the current number and repeat steps 4, 5, and 6. Repeat steps until you get the answer precision (number of decimal places) you need.

    Understanding the Process

      To master this method, imagine the number whose square root you need to find as the area of ​​the square S. In this case, you will look for the length of the side L of such a square. We calculate the value of L such that L² = S.

      Give a letter for each number in the answer. Let us denote by A the first digit in the value of L (the desired square root). B will be the second digit, C the third and so on.

      Specify a letter for each pair of first digits. Let us denote by S a the first pair of digits in the value of S, by S b the second pair of digits, and so on.

      Understand the connection between this method and long division. Just like in division, where we are only interested in the next digit of the number we are dividing each time, when calculating a square root, we work through a pair of digits sequentially (to get the next one digit in the square root value).

    1. Consider the first pair of digits Sa of the number S (Sa = 7 in our example) and find its square root. In this case, the first digit A of the desired value of the square root will be a digit whose square is less than or equal to S a (that is, we are looking for an A such that the inequality A² ≤ Sa< (A+1)²). В нашем примере, S1 = 7, и 2² ≤ 7 < 3²; таким образом A = 2.

      • Let's say we need to divide 88962 by 7; here the first step will be similar: we consider the first digit of the divisible number 88962 (8) and select the largest number that, when multiplied by 7, gives a value less than or equal to 8. That is, we are looking for a number d for which the inequality is true: 7 × d ≤ 8< 7×(d+1). В этом случае d будет равно 1.