Question

find the value of [x root q / x root r] root 1/qr * [x root r / x root p] root 1/rp * [x root p / x root q] root
1/pq
please tell me the answer with the prose's

Answer 1

$( \frac{x \sqrt{q} }{x \sqrt{r}} \times \sqrt{ \frac{1}{qr} } )*( \frac{x \sqrt{r} }{x \sqrt{p}} \times \sqrt{ \frac{1}{rp} } )*( \frac{x \sqrt{p} }{x \sqrt{q}} \times \sqrt{ \frac{1}{pq} } )\\ \\( \frac{ \sqrt{q} }{\sqrt{r}} \times { \frac{1}{ \sqrt{q} \sqrt{r} } } )*( \frac{ \sqrt{r} }{ \sqrt{p}} \times \frac{1}{\sqrt{r} \sqrt{p}} } )*( \frac{ \sqrt{p} }{ \sqrt{q}} \times \frac{1}{\sqrt{p} \sqrt{q}} } )$

$( \frac{1}{ \sqrt{r} } \times \frac{1}{ \sqrt{r} } ) *( \frac{1}{ \sqrt{p} } \times \frac{1}{ \sqrt{p} } ) *( \frac{1}{ \sqrt{q} } \times \frac{1}{ \sqrt{q} } ) \\ \\ = \frac{1}{r} * \frac{1}{p} * \frac{1}{q}\\ \\ = \frac{1}{pqr}$