Square Root of 1033
2026-02-28 10:39 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1033

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 1033, we need to group it as 33 and 10.

Step 2: Now we need to find n whose square is less than or equal to 10. We can say n as ‘3’ because \(3 \times 3 = 9\) is less than or equal to 10. The quotient is 3. After subtracting \(10 - 9\), the remainder is 1.

Step 3: Now, bring down 33, which makes the new dividend 133. Add the old divisor with the same number: \(3 + 3 = 6\), which will be our new divisor.

Step 4: The new divisor will be 6n. Now we need to find the value of n such that \(6n \times n \leq 133\). Let us consider n as 2, now \(62 \times 2 = 124\).

Step 5: Subtract \(133 - 124\); the difference is 9, and the quotient is 32.

Step 6: 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 900.

Step 7: Now we need to find the new divisor that is 644, because \(644 \times 1 = 644\).

Step 8: Subtracting 644 from 900, we get the result 256.

Step 9: Continue doing these steps until we get two numbers after the decimal point. If there is no remaining value, continue until the remainder is zero.

So the square root of √1033 ≈ 32.15598.