Square Root of 1540
2026-02-28 09:05 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1540

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 1540, we need to group it as 40 and 15.

Step 2: Now we need to find n whose square is 15. We can say n is ‘3’ because 3 × 3 is lesser than or equal to 15. Now the quotient is 3 after subtracting 9 (3 × 3) from 15, the remainder is 6.

Step 3: Now let us bring down 40, which is the new dividend. Add the old divisor with the same number 3 + 3, and we get 6, which will be our new divisor.

Step 4: The new divisor will be the sum with a placeholder, making it 60. Now we get 60n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 60n × n ≤ 640. Let us consider n as 1, now 60 × 1 = 60.

Step 6: Subtract 60 from 640, the difference is 580, 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 58000.

Step 8: Now we need to find the new divisor that is 392 because 392 × 9 = 3528.

Step 9: Subtracting 3528 from 5800, we get the result 2272.

Step 10: Now the quotient is 39.2

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 √1540 is approximately 39.24.