If \(x^{1/4}= \frac{1}{p}\) and \(y^{1/2}= \frac{1}{q}\) , what is the value of \(\sqrt{xy}\)

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28-01-2017
Mathematics

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If \(x^{1/4}= \frac{1}{p}\) and \(y^{1/2}= \frac{1}{q}\) , what is the value of \(\sqrt{xy}\)

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LammettHash LammettHash · Answer 1 · 2017-02-01T17:02:39-05:00

LammettHash LammettHash

01-02-2017

\(x^{1/4}=\dfrac1p\implies x=\dfrac1{p^4}\)
\(y^{1/2}=\dfrac1q\implies y=\dfrac1{q^2}\)

\(\implies \sqrt{xy}=\sqrt{\dfrac1{p^4}\times\dfrac1{q^2}}=\dfrac1{p^2q}\)

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