Square Root of 523
2026-02-28 08:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-523

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 523, it remains as 523.

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

Step 3: Now let us bring down 23, making the new dividend 123. Add the old divisor (2) with itself to get 4, which will be our new divisor.

Step 4: Now, we need to find a number n such that 4n x n is less than or equal to 123. Let n be 2, then 42 x 2 = 84.

Step 5: Subtract 84 from 123, the remainder is 39, and the partial quotient is 22.

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 3900.

Step 7: Now we need to find the new divisor. Using trial and error, we find the new divisor to be 445 because 445 x 9 = 4005, which is too large. Using 444 x 8 = 3552, which is closer.

Step 8: Subtract 3552 from 3900 to get 348.

Step 9: Now the quotient is 22.8. Continue doing these steps until you get two numbers after the decimal point or until the remainder is zero.

So, the square root of √523 ≈ 22.85.