Square Root of 11.6
2026-02-28 12:42 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-11.6

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 11.6, we need to consider it as 11.60.

Step 2: Now we need to find n whose square is less than or equal to 11. We can say n as ‘3’ because 3 x 3 = 9 is less than 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.

Step 3: Now let us bring down 60, making the new dividend 260. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 260.

Step 5: Let us consider n as 4, now 64 x 4 = 256.

Step 6: Subtract 256 from 260, the difference is 4, and the quotient is 3.4.

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 400.

Step 8: Now we need to find the new divisor. It will be 68 because 684 x 4 = 2736, and 68 x 5 = 340, which is less than 400.

Step 9: Subtracting 340 from 400 gives the result 60.

Step 10: Now the quotient is approximately 3.40.

Step 11: 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 √11.6 ≈ 3.405877.