Square Root of 151
2026-02-28 01:00 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-151

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 151, we need to group it as 51 and 1.

Step 2: Now we need to find a number whose square is less than or equal to 1. We can say this number is '1' because 1 × 1 is 1. The quotient is 1, and after subtracting 1 from 1, the remainder is 0.

Step 3: Now let us bring down 51, which is the new dividend. Add the old divisor with the same number: 1 + 1, which gives us 2, the new divisor.

Step 4: We get 2n as the new divisor. We need to find a value of n such that 2n × n is less than or equal to 51. Let us consider n as 2, so 22 × 2 = 44.

Step 5: Subtract 44 from 51; the difference is 7, 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 zeroes to the dividend. Now the new dividend is 700.

Step 7: Now we need to find the new divisor. Let us consider 24 as the divisor. If 24 and n = 2, we get 24 × 2 = 48, which is less than 700.

Step 8: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √151 ≈ 12.29.