# How do you simplify sqrt3sqrt21?

May 1, 2018

I get $3 \setminus \sqrt{7}$, see below.

#### Explanation:

Factor the 21 and write each factor as its own square toot:

21=3×7 so \sqrt{21}=\sqrt{3}×\sqrt{7}

You Can't do this with the $\setminus \sqrt{3}$ factor because 3 is,already prime. But you can find a pair of like square roots now in the product $\setminus \sqrt{3} \setminus \sqrt{21}$:

\sqrt{3}\sqrt{21}=\sqrt{3}×(\sqrt{3}×\sqrt{7})

=(\sqrt{3}×\sqrt{3})×\sqrt{7}

=(\sqrt{3})^2×\sqrt{7}

$= \textcolor{b l u e}{3 \setminus \sqrt{7}}$

May 1, 2018

$3 \sqrt{7}$

#### Explanation:

$\text{using the "color(blue)"law of radicals}$

•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)

$\Rightarrow \sqrt{3} \times \sqrt{21} = \sqrt{3 \times 21} = \sqrt{63}$

$\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3 \sqrt{7}$