Square Root of 55.68
2026-02-28 10:50 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-55.68

The long division method is 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, group the numbers from right to left. In the case of 55.68, group it as 55 and 68.

Step 2: Now find n whose square is less than or equal to 55. We can say n as ‘7’ because 7 × 7 = 49, which is less than 55. The quotient is 7; after subtracting 49 from 55, the remainder is 6.

Step 3: Bring down 68, making the new dividend 668. Double the quotient and use it as a new divisor. Hence, 2 × 7 = 14.

Step 4: Find a digit x such that 14x × x ≤ 668. The suitable value is x = 4, so 144 × 4 = 576.

Step 5: Subtract 576 from 668, and the remainder is 92. The quotient is now 7.4.

Step 6: Add a decimal point and bring down two zeros, making the dividend 9200.

Step 7: Double the quotient considering the decimal, making it 148. Find a digit y such that 148y × y ≤ 9200. The suitable value is y = 6, so 1486 × 6 = 8916.

Step 8: Subtract 8916 from 9200, and the remainder is 284.

Step 9: Continue these steps to get two numbers after the decimal point. If there is no remainder, continue until the remainder is zero.

So the square root of √55.68 ≈ 7.46.