Square Root of 2756
2026-02-28 13:51 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2756

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 2756, we need to group it as 56 and 27.

Step 2: Now we need to find n whose square is less than or equal to 27. We can say n as ‘5’ because 5 x 5 = 25, which is less than 27. Now the quotient is 5 after subtracting 25 from 27, the remainder is 2.

Step 3: Now let us bring down 56 to the right of 2, making the new dividend 256. Add the old divisor with the same number 5 + 5, we get 10, which will be our new divisor.

Step 4: The new divisor will be 10n. We need to find the value of n.

Step 5: We find 10n x n ≤ 256. Let us consider n as 2, now 10 x 2 = 20, and 20 x 2 = 40, which is too low. Try n = 5, yielding 105 x 5 = 525, which is too high, so try n = 2, to get 102 x 2 = 204.

Step 6: Subtract 204 from 256, the difference is 52, and the quotient is 52.

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 5200.

Step 8: Now we need to find the new divisor, which is 520 because 520 x 10 = 5200.

Step 9: Subtracting 5200 from 5200, we get the remainder 0.

Step 10: Now the quotient is 52.0

Step 11: Continue doing these steps until the remainder is zero.

So the square root of √2756 is approximately 52.52.