Square Root of 5648
2026-02-28 10:45 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5648

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 5648, we need to group it as 48 and 56.
 

Step 2: Now we need to find n whose square is closest to or less than 56. We can use n as ‘7’ because 7 x 7 is 49, which is less than 56. Now the quotient is 7, and after subtracting 49 from 56, the remainder is 7.

Step 3: Now, let us bring down 48, which is the new dividend. Add the old divisor with the same number (7 + 7) to get 14, which will be our new divisor.

Step 4: The new divisor will be the sum of the current divisor and the next digit of the quotient. Now we get 14n as the new divisor, and we need to find the value of n.

Step 5: The next step is to find 14n x n ≤ 748. Let us consider n as 5 since 145 x 5 = 725, which is closest to 748.

Step 6: Subtract 725 from 748; the difference is 23, and the quotient is 75.

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 2300.

Step 8: Now we need to find the new divisor. We find 150n x n ≤ 2300. Let us consider n as 1 since 1501 x 1 = 1501.

Step 9: Subtracting 1501 from 2300, we get 799.

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue till the remainder is zero.

So the square root of √5648 ≈ 75.146.