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WARRIOR [948]
4 years ago
15

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

Mathematics
1 answer:
Lemur [1.5K]4 years ago
7 0

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

Step-by-step explanation:

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

'

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} .

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