Square Root of 278
2026-02-28 17:10 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-278

The long division method is particularly used for non-perfect square numbers. 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 278, we need to group it as 78 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 is less than 2. Now the quotient is 1, and after subtracting 1 from 2, the remainder is 1.

Step 3: Bring down 78, the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.

Step 4: Now, considering 2n as the new divisor, we need to find the value of n.

Step 5: We need 2n x n ≤ 178. Let us consider n as 6, then 26 x 6 = 156.

Step 6: Subtract 156 from 178; the difference is 22, and the quotient is 16.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to extend the dividend with two zeros. Now the new dividend is 2200.

Step 8: Find the new divisor, which is 333, because 333 x 6 = 1998.

Step 9: Subtracting 1998 from 2200, we get the result 202.

Step 10: Now the quotient is 16.6.

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

So the square root of √278 is approximately 16.67.