Question

Simplify √16n/m^3 1. 4√mn/n^2 2.4√mn/m 3.√mn/4m 4. 4√mn/m^2

Answer 1

Answer: $4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}$ .

Step-by-step explanation:

The given expression: $\sqrt{\dfrac{16n}{m^3}}$

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since $16=4^2$

$m^3=m^{2+1}= m^2\times m$   [$a^{n+m}=a^n\times a^m$]

Now, the given expression becomes,

$\sqrt{\dfrac{4^2n}{m^2\timesn}}=\dfrac{4\sqrt{n}}{m\sqrt{m}}$

Since there is root in denominator , so we need to rationalize

$\dfrac{4\sqrt{n}}{m\sqrt{m}}\times\dfrac{\sqrt{m}}{\sqrt{m}}=\dfrac{4\sqrt{mn}}{m\times\sqrt{m}\times\sqrt{m} }\\\\=\dfrac{4\sqrt{mn}}{m\times m}\\\\=\dfrac{4\sqrt{mn}}{m^2}$

Hence, the correct option is $4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}$ .