Square Root of 5746
2026-02-28 14:02 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5746

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 5746, we need to group it as 46 and 57.

Step 2: Now we need to find n whose square is less than or equal to 57. We can say n as ‘7’ because 7 × 7 = 49 is less than 57. Now the quotient is 7, and after subtracting 49 from 57, the remainder is 8.

Step 3: Now let us bring down 46, making the new dividend 846. Add the old divisor with the same number, 7 + 7, which gives us 14 as the new divisor.

Step 4: The next step is to find 2n × n ≤ 846. Let us consider n as 5, making 145 × 5 = 725.

Step 5: Subtract 725 from 846; the difference is 121.

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 12100.

Step 7: Now we need to find the new divisor that is 150, because 150 × 8 = 1200.

Step 8: Subtracting 1200 from 12100, we get the result 100.

Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.

So the square root of √5746 ≈ 75.80.