Square Root of 9700
2026-02-28 11:01 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9700

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 9700, we need to group it as '00' and '97'.

Step 2: Now we need to find n whose square is less than or equal to 97. We can say n as ‘9’ because 9 x 9 = 81 is less than 97. Now the quotient is 9, and after subtracting 81 from 97, the remainder is 16.

Step 3: Now let us bring down '00', making it 1600, which is the new dividend. Add the old divisor with the same number 9 + 9, we get 18, which will be our new divisor.

Step 4: The new divisor will be 18n, and we now need to find a digit n such that 18n x n is less than or equal to 1600.

Step 5: The next step is finding 18n x n ≤ 1600. Let us consider n as 8. So, 188 x 8 = 1504.

Step 6: Subtract 1504 from 1600; the difference is 96, and the quotient becomes 98.

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 9600.

Step 8: Now we need to find the new divisor. The number 985 fits since 985 x 5 = 4925.

Step 9: Subtracting 4925 from 9600, we get the result 4675.

Step 10: Now the quotient is 98.4.

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

So the square root of √9700 ≈ 98.49.