How do you simplify the expression sqrt3*3sqrt21?

Apr 1, 2016

$9 \sqrt{7}$

Explanation:

Note that $3 \times 7 = 21$

So write the expression as:

$\textcolor{b l u e}{\sqrt{3}} \textcolor{b r o w n}{\times 3 \sqrt{3 \times 7}}$

Combine the square roots

$3 \sqrt{3 \times 3 \times 7}$

$3 \sqrt{{3}^{2} \times 7}$

Not that $\sqrt{{3}^{2}} = 3$

$3 \times 3 \sqrt{7}$

$9 \sqrt{7}$

$\textcolor{red}{\text{Technically this could be } \pm 9 \sqrt{7}}$