Square Root of 5328
2026-02-28 13:58 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5328

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 5328, we need to group it as 28 and 53.

Step 2: Now we need to find a number whose square is closest to 53. We can say n is '7' because 7 x 7 = 49, which is less than 53. Now the quotient is 7, and after subtracting 49 from 53, the remainder is 4.

Step 3: Bring down 28, which is the new dividend. Add the old divisor with the same number: 7 + 7 = 14, which will be our new divisor.

Step 4: The new divisor is 2n. Now we need to find the value of n.

Step 5: The next step is finding 14n x n ≤ 428. Let's consider n as 3, now 143 x 3 = 429, which is greater than 428, so we try n = 2, then 142 x 2 = 284.

Step 6: Subtract 284 from 428; the difference is 144.

Step 7: Since the dividend is not zero, 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 14400.

Step 8: Now we need to find the new divisor, which is 1472 because 1472 x 9 = 13248.

Step 9: Subtract 13248 from 14400; we get the result 1152.

Step 10: Now the quotient is 73.9

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √5328 is approximately 73.