Square Root of 4500
2026-02-28 08:29 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4500

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 4500, we need to group it as 00 and 45.

Step 2: Now we need to find n whose square is less than or equal to 45. We can say n as ‘6’ because 6 × 6 = 36 is less than 45. Now the quotient is 6, and after subtracting 36 from 45, the remainder is 9.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 6 + 6, and we get 12, which will be our new divisor.

Step 4: The new divisor will be 12n. We need to find the value of n such that 12n × n ≤ 900. Let us consider n as 7, 127 × 7 = 889.

Step 5: Subtract 889 from 900, the difference is 11, and the quotient is now 67.

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 1100.

Step 7: Now we need to find the new divisor, which is 134 because 1348 × 8 = 10784.

Step 8: Subtracting 10784 from 11000, we get the result 216.

Step 9: Now the quotient is 67.08.

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

So the square root of √4500 is approximately 67.08.