Square Root of 207
2026-02-28 11:58 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-207

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 207, we need to group it as 07 and 2.

Step 2: Now we need to find n whose square is less than or equal to 2. We can say n is ‘1’ because 1 x 1 = 1, which is less than or equal to 2. Now the quotient is 1, and after subtracting 1 from 2, the remainder is 1.

Step 3: Bring down 07, so the new dividend is 107. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.

Step 4: The new divisor will be 2n. We need to find the value of n such that 2n x n is less than or equal to 107. Let us consider n as 4, now 24 x 4 = 96.

Step 5: Subtract 96 from 107, and the difference is 11. The quotient is 14.

Step 6: Since the dividend is still 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 1100.

Step 7: Now we need to find the new divisor, which is 287 because 287 x 4 = 1148.

Step 8: Subtracting 1148 from 1100 gives -48, but since it is negative, we adjust to get 1100 minus 108 = 992.

Step 9: Now the quotient is 14.3.

Step 10: Continue doing these steps until we get two numbers after the decimal point or the remainder is zero.

So the approximate square root of √207 is 14.39.