Square Root of 171
2026-02-28 19:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-171

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, we need to group the numbers from right to left. In the case of 171, we need to group it as 71 and 1.

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

Step 3: Now let us bring down 71, 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: The new divisor will be 20 since we add a digit and guess n such that 2n x n is less than or equal to 71.

Step 5: The next step is finding 2n x n ≤ 71. Let us consider n as 3, now 23 x 3 = 69.

Step 6: Subtract 71 from 69, the difference is 2, and the quotient is 13.

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 200.

Step 8: Now we need to find the new divisor that is 261 because 261 x 7 ≈ 1827.

Step 9: Subtracting 1827 from 2000, we get the result 173.

Step 10: Now the quotient is 13.0.

Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √171 ≈ 13.08.