Square Root of 824
2026-02-28 11:44 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-824

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 824, we need to group it as 24 and 8.

Step 2: Now, we need to find a number whose square is less than or equal to 8. We can say n as '2' because 2 x 2 = 4, which is less than 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.

Step 3: Bring down 24, making the new dividend 424. Add the old divisor with the quotient, 2 + 2, to get 4, which will be part of our new divisor.

Step 4: The new divisor is 42n. We need to find the value of n such that 42n x n ≤ 424. Let's consider n as 9, then 42 x 9 = 378.

Step 5: Subtract 378 from 424, the difference is 46, and the quotient is 29.

Step 6: Since there is a remainder, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4600.

Step 7: Find a new divisor that is 586 because 586 x 8 = 4688.

Step 8: Subtracting 4688 from 4600 gives the result -88.

Step 9: Continue these steps until we get two numbers after the decimal point or until the remainder is zero. So the square root of √824 is approximately 28.72.