Question

find the value of
$\sqrt[3]{339 + \sqrt[3]{32 \sqrt[3]{8} } }$

Answer 1

Hi friend!!

Given,

$\sqrt[3]{339 + \sqrt[3]{32 \sqrt[3]{8} } }$


$= \sqrt[3]{339 + \sqrt[3]{32 \sqrt[3]{ {2}^{3} } } }$


$= \sqrt[3]{339 + \sqrt[3]{32 \times 2} }$


$= \sqrt[3]{339 + \sqrt[3]{64} }$


$= \sqrt[3]{339 + \sqrt[3]{ {4}^{3} } }$


$= \sqrt[3]{339 + 4}$


$= \sqrt[3]{343}$

$= \sqrt[3]{ {7}^{3} }$

=7

I hope this will help you ;)