Square Root of 1006
2026-02-28 13:03 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1006

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 1006, we need to group it as 06 and 10.

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

Step 3: Now let us bring down 06, 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, we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 106; let us consider n as 1, now 6 x 1 x 1 = 61.

Step 6: Subtract 106 from 61; the difference is 45, 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 4500.

Step 8: Now we need to find the new divisor, which is 317 because 317 x 7 = 2219.

Step 9: Subtracting 2219 from 4500, we get the result 2281.

Step 10: Now the quotient is 31.7

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

So the square root of √1006 is approximately 31.72.