Square Root of 1014
2026-02-28 09:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1014

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 1014, we need to group it as 14 and 10.

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

Step 3: Now let us bring down 14, which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 114. Let us consider n as 1; now 6 × 1 × 1 = 6.

Step 6: Subtract 114 from 6, the difference is 108, 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 10800.

Step 8: Now we need to find the new divisor that is 317 because 317 × 3 = 951.

Step 9: Subtracting 951 from 10800, we get the result 10849.

Step 10: Now the quotient is 31.8.

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

So the square root of √1014 ≈ 31.84