Square Root of 665
2026-02-28 00:46 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-665

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 665, we need to group it as 65 and 6.

Step 2: Now we need to find n whose square is closest to 6. We can say n as ‘2’ because 2 x 2 is lesser than or equal to 6. Now the quotient is 2, after subtracting 4 from 6 the remainder is 2.

Step 3: Now let us bring down 65 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 x n ≤ 265. Let's consider n as 6, now 46 x 6 = 276, which is more than 265, so consider n as 5. Now, 45 x 5 = 225.

Step 6: Subtract 225 from 265, the difference is 40, and the quotient is 25.

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 4000.

Step 8: Now we need to find the new divisor that is 515 because 515 x 5 = 2575.

Step 9: Subtracting 2575 from 4000 we get the result 1425.

Step 10: Now the quotient is 25.7.

Step 11: Continue doing these steps until we get the desired precision.

So the square root of √665 is approximately 25.77.