Which of the following expressions is the simplified form of the given expression, given that $m$ and $n$ are positive?
$\sqrt{9 m^{5} n^{2} - m^{4} n^{2}}$

3 \sqrt{m}

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3 m n

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3 n \sqrt{m}

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m^{2} n \sqrt{9 m - 1}

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Solution

The correct option is D $m^{2} n \sqrt{9 m - 1}$

We need to simplify $\sqrt{9 m^{5} n^{2} - m^{4} n^{2}}$ as
$\Rightarrow \sqrt{m^{4} n^{2} (9 m - 1)}$
$\Rightarrow m^{2} n \sqrt{(9 m - 1)}$

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