Square Root of 276
2026-02-28 23:12 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-276

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 276, we need to group it as 76 and 2.

Step 2: Now we need to find n whose square is 2. We can say n as ‘1’ because 1 × 1 is lesser than or equal to 2. Now the quotient is 1, and after subtracting 1² from 2, the remainder is 1.

Step 3: Now let us bring down 76, which is the new dividend. Add the old divisor with the same number, 1 + 1, we get 2, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 176. Let us consider n as 6; now, 26 × 6 = 156.

Step 6: Subtract 176 from 156, the difference is 20, 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 add two zeroes to the dividend. Now the new dividend is 2000.

Step 8: Now we need to find the new divisor which is 132 because 266 × 7 = 1862.

Step 9: Subtracting 1862 from 2000, we get the result 138.

Step 10: Now the quotient is 16.7.

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

So the square root of √276 is approximately 16.61.