Find the nearest integer to the square root of $232$ .

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Solution

We know, $15^{2} = 225$ and $16^{2} = 256$
Also we have, $225 < 232 < 256$
$⟹ 15^{2} < 232 < 16^{2}$
Difference of $225$ and $232$ is $7$ whereas difference of $256$ and $232$ is $24$ .
So, the square root of $232$ is nearest to $15$ .
Hence, the answer is $15$

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