Square Root of 1083
2026-02-28 13:34 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1083

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 1083, we need to group it as 83 and 10.

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

Step 3: Now let us bring down 83, making the new dividend 183. Add the previous divisor (3) with the same number to get 6, which will be our new divisor.

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

Step 5: The next step is finding 6n × n ≤ 183. Let us consider n as 3; now, 63 × 3 = 189, which is too large. Trying n as 2, we get 62 × 2 = 124.

Step 6: Subtract 124 from 183; the difference is 59, and the quotient is 32.

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 5900.

Step 8: Find the new divisor, which is 649, because 649 × 9 = 5841. Step 9: Subtracting 5841 from 5900, we get the result 59.

Step 10: Now the quotient is 32.9.

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 √1083 is approximately 32.89.