Question

Simplify:
$\sqrt{18}\times \sqrt{27}\times \sqrt{128}$.

Answer 1

The given surds can be simplified as follows:

$\sqrt{18}\times \sqrt{27}\times \sqrt{128}=\sqrt{9\times 2}\times \sqrt{9\times 3}\times \sqrt{64\times 2}=3\sqrt{2}\times 3\sqrt{3}\times 8\sqrt{2}=(3\times 3\times 8)\times \left(\sqrt{2\times 3\times 2}\right)=72\sqrt{12}$

$=72\sqrt{4\times 3}=72\times 2\sqrt{3}=144\sqrt{3}$.

Hence, $\sqrt{18}\times \sqrt{27}\times \sqrt{128}=144\sqrt{3}$.