Square Root of 500
2026-02-28 13:40 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-500

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 500, we need to group it as 00 and 5.

Step 2: Now we need to find n whose square is less than or equal to 5. We can say n is ‘2’ because 2 x 2 = 4, which is less than or equal to 5. Now the quotient is 2, and after subtracting 5 - 4, the remainder is 1.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 2 + 2, we get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n × n ≤ 100. Let us consider n as 2, now 4 x 2 x 2 = 84.

Step 6: Subtract 100 from 84, the difference is 16, and the quotient is 22.

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 1600.

Step 8: Now we need to find the new divisor that is 9 because 449 x 9 = 4041.

Step 9: Subtracting 4041 from 1600, we get the result 159.

Step 10: Now the quotient is 22.3.

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 √500 is approximately 22.36.