Question

Compare the values given in the image

Answer 1

Answer:

Explanation

Step-by-step explanation:

$\sqrt[4]{9}$

:

$\sqrt[6]{21}$

=1.73 : 1.66

So the first one is greater

Answer 2

$\mathrm{L.C.M. \: of \: index \: or \: power \: 4 \: and \: 6 \: = \: 12}$

$\mathrm{Now,}$

$\sqrt[4]{9} = {(9)}^{ \frac{1}{4} } = ({9}^{3})^{ \frac{1}{12} } = ( {729})^{ \frac{1}{12} }$

$\sqrt[6]{21} = {(21)}^{ \frac{1}{6} } = ({21}^{2})^{ \frac{1}{12} } = ( {441})^{ \frac{1}{12} }$

$\mathrm{Therefore,}$

$\sqrt{729}^{ \frac{1}{12} } > \sqrt{441} ^{ \frac{1}{12} }$

$\sqrt[4]{9} > \sqrt[6]{21}$