Square Root of 1500
2026-02-28 10:13 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1500

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 1500, we need to group it as 00 and 15.

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

Step 3: Now let us bring down 00, 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 ≤ 600. Let us consider n as 9, now 69 x 9 = 621.

Step 6: Subtract 621 from 600, the difference is 21, and the quotient is 38.

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 2100.

Step 8: Now we need to find the new divisor that is 387 because 387 x 5 = 1935.

Step 9: Subtracting 1935 from 2100, we get the result 165.

Step 10: Now the quotient is 38.7.

Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √1500 is approximately 38.73.