Square Root of 9100
2026-02-28 08:38 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9100

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 9100, we need to group it as 00 and 91.

Step 2: Now we need to find n whose square is less than or equal to 91. We consider n as '9' because 9 x 9 = 81 is less than 91. Now the quotient is 9, and after subtracting 81 from 91, the remainder is 10.

Step 3: Now let us bring down 00 to make the new dividend 1000. Add the old divisor, 9, with the same number 9 + 9, we get 18, which will be our new divisor.

Step 4: The new divisor will be 18n, where we need to find the value of n such that 18n x n is less than or equal to 1000.

Step 5: The next step is finding 18n x n ≤ 1000. Let us consider n as 5, then 185 x 5 = 925.

Step 6: Subtract 925 from 1000, the difference is 75, and the quotient is 95.

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 7500.

Step 8: Now we need to find the new divisor, which is 953, because 953 x 8 = 7624.

Step 9: Subtracting 7624 from 7500 gives us a negative remainder, so we adjust n to 7 and get 952 x 7 = 6664.

Step 10: Subtracting 6664 from 7500, we get the remainder 836.

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

So, the square root of √9100 is approximately 95.39.