Square Root of 155
2026-02-28 10:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-155

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 155, we need to group it as 55 and 1.

Step 2: Now we need to find n whose square is less than or equal to 1. We can say n is ‘1’ because 1 x 1 is lesser than or equal to 1. Now the quotient is 1, after subtracting 1 - 1, the remainder is 0.

Step 3: Now let us bring down 55, which is the new dividend. Add the old divisor with the same number 1 + 1; we get 2, which will be our new divisor.

Step 4: We need to find a number n such that 2n x n ≤ 55. Let us consider n as 2, now 22 x 2 = 44.

Step 5: Subtract 44 from 55; the difference is 11, and the quotient is 12.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 1100.

Step 7: Now we need to find the new divisor, which is 249, because 249 x 4 = 996.

Step 8: Subtracting 996 from 1100, we get the result 104.

Step 9: Now the quotient is 12.4.

Step 10: 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 √155 is approximately 12.45.