Square Root of 1017
2026-02-28 08:19 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1017

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 1017, we need to group it as 17 and 10.

Step 2: Now we need to find n whose square is less than or equal to 10. We can say n is 3 because 3 x 3 = 9 is less than 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.

Step 3: Now let us bring down 17, which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: The new divisor will be 6n, where n is to be determined.

Step 5: The next step is finding 6n x n ≤ 117. Let us consider n as 1, so 6 x 1 x 1 = 6.

Step 6: Subtract 117 from 6, the difference is 111, and the quotient is 31.

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 11100.

Step 8: Now we need to find the new divisor, which is 618 because 618 x 1 = 618.

Step 9: Subtracting 618 from 11100 gives the result 10482.

Step 10: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √1017 ≈ 31.89.