How do you simplify #root3(3/4)#?

2 Answers
Apr 23, 2017

Answer:

#root(3)(3/4) = root(3)(6)/2#

Explanation:

For any non-zero values of #a, b# we have:

#root(3)(a/b) = root(3)(a)/root(3)(b)#

#root(3)(a^3) = a#

So we find:

#root(3)(3/4) = root(3)((3*2)/(4*2)) = root(3)(6/2^3) = root(3)(6)/root(3)(2^3) = root(3)(6)/2#

Notice how making the denominator into a perfect cube before splitting the radical allows us to avoid having to rationalise the denominator afterwards.

Apr 23, 2017

Answer:

#color(blue)(root3(6)/2#

Explanation:

#root3(3/4)#

#:.=root3(3)/root3(4) xx root3(4)/root3(4) xx root3(4)/root3(4)#

#:.=color(blue)(root3(4)*root3(4)*root3(4)=4#

#:.=root3(48)/4#

#:.=root3(3*2*2*2*2)/4#

#:.=(cancel2^color(blue)1root3(6))/cancel4^color(blue)2#

#:.=color(blue)(root3(6)/2#