Square Root of 172
2026-02-28 09:00 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-172

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 172, we need to group it as 72 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 less than or equal to 1. Now the quotient is 1, and after subtracting 1-1, the remainder is 0.

Step 3: Now let us bring down 72, which is the new dividend. Add the old divisor with the same number: 1 + 1 = 2, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 2n x n ≤ 72. Let us consider n as 3, now 2 x 3 x 3 = 18.

Step 6: Subtract 18 from 72, the difference is 54, 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 5400.

Step 8: Now we need to find the new divisor, which is 26, because 26 x 26 = 676.

Step 9: Subtracting 676 from 5400, we get the result 4724.

Step 10: Now the quotient is 13.1.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue until the remainder is zero.

So the square root of √172 is approximately 13.11.