Square Root of 53.21
2026-02-28 01:19 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-53.21

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 53.21, we treat it as 53 and 21.

Step 2: Now we need to find n whose square is less than or equal to 53. We can say n is 7 because 7 x 7 = 49, which is less than 53.

Step 3: Subtract 49 from 53, and the remainder is 4. Bring down the 21, making it 421.

Step 4: Double the quotient obtained in Step 2, which is 7, to get 14.

Step 5: Now, determine a digit x such that 14x * x ≤ 421. The value of x is 2, because 142 * 2 = 284.

Step 6: Subtract 284 from 421 to get a remainder of 137.

Step 7: Since the remainder is less than the divisor, add a decimal point and bring down two zeros, making it 13700.

Step 8: The new divisor is 144 (142 plus 2), and find x such that 144x * x ≤ 13700. After iterations, the value of x is found to be 9.

Step 9: Subtract and continue the process to find more decimal places as needed.

So the square root of √53.21 is approximately 7.296.