Square Root of 34.57
2026-02-28 09:11 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-34.57

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, group the numbers from right to left. In the case of 34.57, consider it as 34 and 57.

Step 2: Find n whose square is less than or equal to 34. We can say n is 5 because 5 × 5 = 25, which is less than 34. Now the quotient is 5, and after subtracting 25 from 34, the remainder is 9.

Step 3: Bring down 57, making it the new dividend 957. Add the old divisor with the same number: 5 + 5 = 10, which will be our new divisor.

Step 4: The new divisor will be 10n. We need to find the value of n such that 10n × n is less than or equal to 957. Let n be 9, so 109 × 9 = 981. Since 981 is greater than 957, try n = 8, making 108 × 8 = 864.

Step 5: Subtract 864 from 957; the difference is 93, and the quotient is 5.8.

Step 6: Since the dividend is less than the divisor, add a decimal point, allowing us to add two zeroes to the dividend. The new dividend is 9300.

Step 7: Find the new divisor. 108n becomes 1088, and n is 8 because 1088 × 8 = 8704.

Step 8: Subtracting 8704 from 9300 gives the result of 596.

Step 9: Continue doing these steps until you get two numbers after the decimal point.

So the square root of √34.57 is approximately 5.879.