Question

Find the cube root of
$135\sqrt{3}-87\sqrt{6}$

Answer 1

$153\sqrt{3}-87\sqrt{6}$

$=81\sqrt{3}+54\sqrt{3}-81\sqrt{6}-6\sqrt{6}$

$=(3\sqrt{3}{)}^3+(-\sqrt{6}{)}^3+3\times 3\sqrt{3}\times (-\sqrt{6})(3\sqrt{3}-\sqrt{6})$

$=(3\sqrt{3}-\sqrt{6}{)}^3$

Hence Cube root is $3\sqrt{3}-\sqrt{6}$