Square Root of 13500
2026-02-28 23:24 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-13500

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, we need to group the numbers from right to left. In the case of 13500, we need to group it as 500 and 13.

Step 2: Now we need to find n whose square is ≤ 13. We can say n is ‘3’ because 3 x 3 = 9, which is less than or equal to 13. Now the quotient is 3, and after subtracting 9 from 13, the remainder is 4.

Step 3: Now let us bring down 500, which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

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

Step 5: The next step is finding 6n x n ≤ 450. Let us consider n as 7, now 67 x 7 = 469.

Step 6: Subtract 450 from 469, and the difference is 19, with a quotient of 37.

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 1900.

Step 8: Now we need to find the new divisor that is 746 because 746 x 2 = 1492.

Step 9: Subtracting 1492 from 1900, we get the result 408.

Step 10: Now the quotient is 116.2.

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 √13500 is approximately 116.19.