Square Root of 527
2026-02-28 08:37 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-527

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root of 527 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 527, we need to group it as 27 and 5.

Step 2: Now, we need to find n whose square is less than or equal to 5. We can say n is '2' because 2 x 2 is 4, which is less than 5. The quotient is 2, and the remainder is 1.

Step 3: Bring down 27, making the new dividend 127. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor prefix.

Step 4: Find a number n such that 4n x n is less than or equal to 127. Let n be 2, because 42 x 2 = 84.

Step 5: Subtract 84 from 127, the difference is 43, and the quotient is 22.

Step 6: Since the dividend is less than the divisor, we add a decimal point and two zeroes, making the new dividend 4300.

Step 7: Find a new divisor prefix which is 44, because 449 x 9 = 4041.

Step 8: Subtract 4041 from 4300 to get the result 259.

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

So, the square root of √527 is approximately 22.96.