How do you simplify root3(3/4)3√34?
2 Answers
Apr 23, 2017
Explanation:
For any non-zero values of
root(3)(a/b) = root(3)(a)/root(3)(b)3√ab=3√a3√b
root(3)(a^3) = a3√a3=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)/23√34=3√3⋅24⋅2=3√623=3√63√23=3√62
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
