Question

Find the cube root of
$10+6\sqrt{3}$

Answer 1

$10+6\sqrt{3}$

$=1+9+3\sqrt{3}+3\sqrt{3}$

$=(\sqrt{3}{)}^3+1^3+3\times (\sqrt{3}{)}^2\times 1+3\times \sqrt{3}\times 1^2$

$=(1+\sqrt{3}{)}^3$

Hence, cube root of $10+6\sqrt{3}$ is $1+\sqrt{3}$