How do you simplify #sqrt3*sqrt6#?

3 Answers
Jim G.
May 29, 2017

#3sqrt2#

Explanation:

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

#color(orange)"Reminder" sqrtaxxsqrtbhArrsqrt(ab)#

#rArrsqrt3xxsqrt6=sqrt(3xx6)=sqrt18#

#sqrt18=sqrt(9xx2)=sqrt9xxsqrt2=3xxsqrt2#

#rArrsqrt3xxsqrt6=3sqrt2#

EZ as pi
May 29, 2017

#=3sqrt2#

Explanation:

Remember that if you multiplying or dividing square roots, you can combine them into one.

#sqrt3 xx sqrt6 = sqrt(3xx6)" "larr# factor #6#

#= sqrt (3xx3xx2) = sqrt(3^2xx2) #

Now find the roots where possible:

#=3sqrt2#

Barney V.
May 29, 2017

#color(blue)(=3sqrt2#

Explanation:

#sqrt3*sqrt6#

#:.=sqrt(6*3)#

#:.=sqrt(2*ul(3*3))#

#:.=sqrt3 xx sqrt3=3#

#:.color(blue)(=3sqrt2#

check:

#:.color(blue)(sqrt3 xx sqrt6=4.242640687#

#:.color(blue)(3 xx sqrt2 =4.242640687#

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