Square Root of 667
2026-02-28 10:09 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-667

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 667, we need to group it as 67 and 6.

Step 2: Now we need to find n whose square is 6. We can say n as ‘2’ because 2x2 is lesser than or equal to 6. Now the quotient is 2 and after subtracting 6-4 the remainder is 2.

Step 3: Now let us bring down 67 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 ≤ 267. Let us consider n as 6, now 46x6 = 276, which is larger, so let’s try n as 5, now 45x5 = 225.

Step 6: Subtract 267 from 225, the difference is 42, 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 4200.

Step 8: Now we need to find the new divisor that is 519 because 519x8 = 4152.

Step 9: Subtracting 4152 from 4200 we get the result 48.

Step 10: Now the quotient is 25.8.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √667 is approximately 25.82.