Square Root of 1021
2026-02-28 17:18 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1021

The long division 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 square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 1021, we need to group it as 21 and 10.

Step 2: Now we need to find n whose square is less than or equal to 10. We can say n as ‘3’ because 3 × 3 = 9, which is lesser than 10. Now the quotient is 3. After subtracting 9 from 10, the remainder is 1.

Step 3: Now let us bring down 21 which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6 which will be our new divisor.

Step 4: The new divisor will be 6. We need to find n such that 6n × n ≤ 121. Let us consider n as 1, now 61 × 1 = 61.

Step 5: Subtract 61 from 121; the difference is 60, and the quotient is 31.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 6000.

Step 7: Now we need to find the new divisor, which is 639 because 639 × 9 = 5751.

Step 8: Subtracting 5751 from 6000, we get the result 249.

Step 9: Now the quotient is 31.9

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.

So the square root of √1021 ≈ 31.95