Square Root of 9225
2026-02-28 10:12 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9225

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 9225, we need to group it as 25 and 92.

Step 2: Now we need to find n whose square is less than or equal to 92. We can say n is ‘9’ because 9 x 9 = 81, which is less than 92. Now the quotient is 9, and after subtracting 81 from 92, the remainder is 11.

Step 3: Now, let us bring down 25, which becomes the new dividend. Add the old divisor with the same number 9 + 9 to get 18, which will be our new divisor.

Step 4: The new divisor will be represented as 18n. We need to find the value of n such that 18n x n ≤ 1125.

Step 5: The next step is finding 18n × n ≤ 1125. Let us consider n as 6, now 186 x 6 = 1116.

Step 6: Subtract 1116 from 1125; the difference is 9, and the quotient becomes 96.

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 zeroes to the dividend. Now, the new dividend is 900.

Step 8: Now we need to find the new divisor, which is 193, because 193 x 4 = 772.

Step 9: Subtracting 772 from 900, we get the result 128.

Step 10: Now the quotient is 96.0.

Step 11: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √9225 is approximately 96.06.