Square Root of 274
2026-02-28 13:13 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-274

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 274, we need to group it as 74 and 2.

Step 2: Now we need to find n whose square is 2. We can say n as ‘1’ because 1x1 is less than or equal to 2. Now the quotient is 1; after subtracting 1 from 2, the remainder is 1.

Step 3: Now let us bring down 74, which is the new dividend. 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 ≤ 174. Let us consider n as 6, now 26 x 6 = 156.

Step 5: Subtract 156 from 174; the difference is 18, and the quotient is 16.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 1800.

Step 7: Now we need to find the new divisor that is 9 because 329 x 9 = 2961.

Step 8: Subtracting 2961 from 1800 is not possible, so we adjust and repeat the process for further precision.

Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no more decimal values; continue till the remainder is zero.

So the square root of √274 ≈ 16.55