How do you simplify #sqrt3sqrt21#?

2 Answers
May 1, 2018

Answer:

I get #3\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 #\sqrt{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}#:

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

#=(\sqrt{3}×\sqrt{3})×\sqrt{7}#

#=(\sqrt{3})^2×\sqrt{7}#

#=color(blue)(3\sqrt{7})#

May 1, 2018

Answer:

#3sqrt7#

Explanation:

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

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

#rArrsqrt3xxsqrt21=sqrt(3xx21)=sqrt63#

#sqrt63=sqrt(9xx7)=sqrt9xxsqrt7=3sqrt7#