Square Root of 103
2026-02-28 11:48 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-103

The long division method is particularly used for non-perfect square numbers. This method involves finding the closest perfect square number for the given number. Let us now learn how to find the square root of 103 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 103, we treat it as a single group because it has only three digits.

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

Step 3: Bring down 3 next to the remainder, making it 13. Add the old divisor with the same number, 3 + 3, to get 6 as the new divisor.

Step 4: The new divisor is 6n. We need to find the value of n. Try n = 2, so 6 × 2 = 12, which is less than or equal to 13.

Step 5: Subtract 12 from 13, and the remainder is 1. The quotient becomes 10.2.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point and bring down two zeros, making the new dividend 100.

Step 7: The new divisor will be 62. Try n = 1, so 62 × 1 = 62.

Step 8: Subtract 62 from 100, leaving a remainder of 38.

Step 9: Continue doing these steps until we get the desired precision.

We find the square root of √103 ≈ 10.14889.