Square Root of 664
2026-02-28 11:00 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-664

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 664, we need to group it as 64 and 6.

Step 2: Now we need to find n whose square is ≤ 6. We can say n as ‘2’ because 2 x 2 = 4, which is less than or equal to 6. Now the quotient is 2, and the remainder is 6 - 4 = 2.

Step 3: Now let us bring down 64, 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 previous quotient and the next digit of the dividend. Now we get 4n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 4n x n ≤ 264. Let us consider n as 6; now, 4 x 6 x 6 = 144.

Step 6: Subtract 264 from 144; the difference is 120, and the quotient is 26.

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 12000.

Step 8: Now we need to find the new divisor that is 53 because 532 x 3 = 159.

Step 9: Subtracting 159 from 1200, we get the result 1041.

Step 10: Now the quotient is 25.7.

Step 11: 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 √664 is approximately 25.77.