How do you simplify sqrt3sqrt21√3√21?

2 Answers
Oscar L.
May 1, 2018

I get 3\sqrt{7}3√7, see below.

Explanation:

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

21=3×721=3×7 so \sqrt{21}=\sqrt{3}×\sqrt{7}√21=√3×√7

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

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

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

=(\sqrt{3})^2×\sqrt{7}=(√3)2×√7

=color(blue)(3\sqrt{7})=3√7

Jim G.
May 1, 2018

3sqrt73√7

Explanation:

"using the "color(blue)"law of radicals"using the law of radicals

•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)∙x√a×√b⇔√ab

rArrsqrt3xxsqrt21=sqrt(3xx21)=sqrt63⇒√3×√21=√3×21=√63

sqrt63=sqrt(9xx7)=sqrt9xxsqrt7=3sqrt7√63=√9×7=√9×√7=3√7

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