How do you simplify sqrt 21 times sqrt 3?

Mar 29, 2016

$\pm 3 \sqrt{7}$

Explanation:

Notice that $3 \times 7 = 21$

Write as:$\text{ } \sqrt{3 \times 7} \times \sqrt{3}$

This is the same as

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

Which is the same as

$\text{ } {\left(\sqrt{3}\right)}^{2} \times \sqrt{7}$

$\text{ } 3 \sqrt{7}$

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Note that if $\sqrt{3}$ is negative then ${\left(\sqrt{3}\right)}^{2}$ is positive so the 3 is definitely positive.

However, $\sqrt{7}$ stands on its own so we have $\pm \sqrt{7}$

Thus $3 \sqrt{7} \text{ is more correctly written as } \pm 3 \sqrt{7}$