Question

what is the value of √3 ÷⁴√5​

Answer 1

Answer:

tex}\sqrt 2 ,\root 3 \of 4 ,\root 4 \of 3 {/tex}

= {tex}{2^{{1 \over 2}}},{4^{{1 \over 3}}},{3^{{1 \over 4}}}{/tex}

= {tex}{2^{{6 \over {12}}}},{4^{{4 \over {12}}}},{3^{{3 \over {12}}}}{/tex} [Making all the powers as like terms]

= {tex}\root {12} \of {{2^6}} ,\root {12} \of {{4^4}} ,\root {12} \of {{3^3}} {/tex}

= {tex}\root {12} \of {64} ,\root {12} \of {256} ,\root {12} \of {27} {/tex}

Here {tex}\root {12} \of {256} {/tex} is greater.

Therefore, {tex}\root 3 \of 4 {/tex} is greater.