Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 - The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.

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2 - Step 1:To begin with, we need to group the numbers from right to left. In the case of 592, we group it as 92 and 5.

3 - Step 2:Now we need to find n whose square is<a>less than</a>or equal to 5. We can say n as ‘2’ because 2 x 2 = 4, which is less than or equal to 5. Now the<a>quotient</a>is 2; after subtracting 5 - 4, the<a>remainder</a>is 1.

4 - Step 3:Now let us bring down 92, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 to get 4, which will be our new divisor.

5 - Step 4:The new divisor will be in the form of 4n. We need to find the value of n.

6 - Step 5:The next step is finding 4n x n ≤ 192. Let us consider n as 4; now 4 x 4 x 4 = 176.

7 - Step 6:Subtract 192 from 176; the difference is 16, and the quotient is 24.

8 - Step 7:Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 1600.

9 - Step 8:Now we need to find a new divisor, which is 3, because 483 x 3 = 1449.

10 - Step 9:Subtracting 1449 from 1600, we get the result 151.

11 - Step 10:Now the quotient is 24.3.

12 - Step 11:Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

13 - So the square root of √592 is approximately 24.33.

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