Question

Find the value of:

$2\left(6\right(\sqrt{3}{)}^5\left)\right)\left(\sqrt{3}\right)+20\times \left(\sqrt{3}{)}^3\right(\sqrt{2}{)}^3+6\left(\sqrt{3}\right)(\sqrt{2}{)}^5$

Answer 1

$2\left(6\right(\sqrt{3}{)}^5\left)\right(\sqrt{3}\left)\right)+20\times \left(\sqrt{3}{)}^3\right(\sqrt{2}{)}^3+6\left(\sqrt{3}\right)(\sqrt{2}{)}^5$

$=2(6\times (\sqrt{3}{)}^4\left(\sqrt{3}\right))+20\times (\sqrt{3}{)}^2\left(\sqrt{3}\right)\left(\sqrt{2}{)}^2\right(\sqrt{2})+6(\sqrt{3}\left)\right(\sqrt{2}{)}^4\left(\sqrt{2}\right)$

$=2(6\times 9)\sqrt{3}+20\left(3\right)\left(2\right)\left(\sqrt{6}\right)+6\left(\sqrt{6}\right)\left(4\right)$

$=108\sqrt{3}+120\sqrt{6}+24\sqrt{6}$

$=108\sqrt{3}+144\sqrt{6}$