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Multiply $2\sqrt{7}\cdot3\sqrt{21}\text{.}$

To type $\sqrt{\phantom{x}}\text{,}$ use sqrt( ).

Solution

First, multiply the non-radical factors together and the radical factors together. Then look for further simplifications.

$\begin{aligned} 2\sqrt{7}\cdot3\sqrt{21}\amp=2\cdot3\cdot\sqrt{7}\cdot\sqrt{21}\\ \amp=6\cdot\sqrt{7}\cdot\sqrt{7\cdot3}\\ \amp=6\sqrt{7\cdot7\cdot3}\\ \amp=6\cdot7\cdot\sqrt{3}\\ \amp=42\sqrt{3} \end{aligned}$