Square Root of 3176
2026-02-28 08:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3176

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 3176, we need to group it as 76 and 31.

Step 2: Now we need to find n whose square is 31. We can say n as ‘5’ because 5 x 5 = 25, which is less than or equal to 31. Now the quotient is 5, and after subtracting 31 - 25, the remainder is 6.

Step 3: Now let us bring down 76, which is the new dividend. Add the old divisor with the same number: 5 + 5 = 10, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 10n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 10n x n ≤ 676. Let us consider n as 6. Now 106 x 6 = 636.

Step 6: Subtract 676 from 636, and the difference is 40, and the quotient is 56.

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 4000.

Step 8: Now we need to find the new divisor, which is 563.5, because 5635 x 5 = 28175.

Step 9: Subtracting 28175 from 40000, we get the result 11825.

Step 10: Now the quotient is 56.3.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue until the remainder is zero. So, the square root of √3176 is approximately 56.36.