Square Root of 604
2026-02-28 15:47 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-604

The long division method is particularly useful 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 604, we group it as 04 and 6.

Step 2: Find n whose square is less than or equal to 6. We can select n as 2 because 2 x 2 = 4, which is less than 6. The quotient is 2, and the remainder is 6 - 4 = 2.

Step 3: Bring down the next pair, which is 04. Now the new dividend is 204. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find n such that 4n x n ≤ 204. Let's consider n as 5; then, 45 x 5 = 225, which is greater than 204. So, we try n as 4; then, 44 x 4 = 176.

Step 5: Subtract 176 from 204. The difference is 28, and the quotient is 24.

Step 6: Since the dividend is less than the divisor, add a decimal point. Add two zeroes to the dividend, making it 2800.

Step 7: Find the new divisor: 488 x 6 = 2928, which is more than 2800. Try 487 x 5 = 2435.

Step 8: Subtract 2435 from 2800, getting 365. Bring down two more zeroes, making it 36500.

Step 9: Continue doing these steps until we get the desired number of decimal places. So, √604 is approximately 24.576.