Question

compare √
$\sqrt[ 5]{15}$
and
$\sqrt[4]{12}$




​

Answer 1

$\sqrt[4]{12} > \sqrt[5]{15}$

Step-by-step explanation:

Given :

$\sqrt[5]{15} \: \: and \: \: \: \sqrt[4]{12}$

To compare :

Which one is greater..

Solution :

LCM of 5 and 4 = 20.

$\sqrt[5]{15} = \sqrt[5]{ \sqrt[4]{ {15}^{4} } } \: \: and \: \\ \sqrt[4]{12} \: \: \: = \: \sqrt[4]{ \sqrt[5]{ {12}^{5} } }$

$\sqrt[5]{15} = {(50625)}^{ \frac{1}{20} } \: \: and \\ \sqrt[4]{12} = {(248832)}^{ \frac{1}{20} }$

Hence,

$\sqrt[4]{12} > \sqrt[4]{15}$