Question

Find the decimal form of $\sqrt{23}$ and $\sqrt{24}$ correct up to 3 decimal places.

Answer 1

Hint: Write 23 as 23.000000 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. Do a similar process for finding the square root of 24.

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 $\sqrt{23}$ is as follows:

Hence the square root of 23 accurate up to three decimal places is 4.795
The long division method for finding $\sqrt{24}$ is as follows

Hence the square root of 24 accurate up to 3 decimal places is 4.899

Note: Verification:
We have ${{4.795}^{2}}=22.992\approx 23$
Hence, we have
$\sqrt{23}\approx 4.795$
We have ${{4.899}^{2}}=24.000201\approx 24$
Hence, we have
$\sqrt{24}=4.899$
Hence our answer is verified to be correct.