Question

Find the square root of 496 correct up to 3 decimal places.

Answer 1

Hint: Write 496 as 496.00000000 and use a long division method to find the approximate square root of the number up to one more than the desired number of decimal places. Round off the square root and hence find the square root correct up to three decimal places

Complete step-by-step answer:
We follow three simple steps to find the square root of a non-perfect number.
Step 1: Add a suitable number of zeros after the decimal point.
Step 2: Find the approximate square root of the number up to one more than the desired number of decimal places using the long division method.
Step 3: Round off the square root and hence find the value correct up to three decimal places.
The long division method for finding $\sqrt{496}$ is as follows:

Hence the square root of 496 accurate up to three decimal places is 22.271

Note: Verification:
We can verify that the solution is correct by checking that the square of 22.271 is very close to 496.
We have ${{22.271}^{2}}=495.997\approx 496$
Hence, we have
$\sqrt{496}\approx 22.271$
Hence our answer is verified to be correct.