Answer: [tex]4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}[/tex] .
Step-by-step explanation:
The given expression: [tex]\sqrt{\dfrac{16n}{m^3}}[/tex]
'
since [tex]16=4^2[/tex]
[tex]m^3=m^{2+1}= m^2\times m[/tex] [[tex]a^{n+m}=a^n\times a^m[/tex]]
Now, the given expression becomes,
[tex]\sqrt{\dfrac{4^2n}{m^2\timesn}}=\dfrac{4\sqrt{n}}{m\sqrt{m}}[/tex]
Since there is root in denominator , so we need to rationalize
[tex]\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}[/tex]
Hence, the correct option is [tex]4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}[/tex] .
