Square Root of 1530
2026-02-28 17:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1530

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 1530, we need to group it as 30 and 15.

Step 2: Now we need to find n whose square is close to 15. We can say n as ‘3’ because 3 × 3 = 9 is less than 15. Now the quotient is 3 after subtracting 9 from 15, the remainder is 6.

Step 3: Now let us bring down 30, which is the new dividend. Add the old divisor with the same number, 3 + 3, we get 6, which will be our new divisor.

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

Step 5: The next step is finding 6n × n ≤ 630; let us consider n as 1, now 6 × 1 × 1 = 61.

Step 6: Subtract 630 from 61; the difference is 569, 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 56900.

Step 8: Now we need to find the new divisor that is 623 because 623 × 9 = 5607.

Step 9: Subtracting 5607 from 5690, we get the result 83.

Step 10: Now the quotient is 39.1.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values, continue till the remainder is zero.

So the square root of √1530 ≈ 39.12.