How do you simplify #root3(x) / root 3(2)#?

2 Answers
Apr 15, 2017

Answer:

#root3(x/2)#

Explanation:

#sqrt(a)/sqrt(b) = sqrt(a/b)#

Apr 15, 2017

Answer:

#(root(3)(4x))/2#

Explanation:

Usually, you do not want a radical in the denominator. In other words, you usually want to rationalize the denominator.

Here, the fraction can be expressed as #x^(1/3)/2^(1/3)#. If you multiply this by #2^(2/3)/2^(2/3)# (which is equal to #1#), the denominator is rationalized. To see how, remember that #a^b*a^c=a^(b+c)#. Then, #x^(3/2)/2^(3/2)*2^(1/2)/2^(1/2)=(x^(1/3)*2^(2/3))/(2^(1/3)*2^(2/3))=(x^(1/3)*2^(2/3))/(2^(1/3+2/3))=(x^(1/3)*2^(2/3))/4=(x^(1/3)*2^(2/3))/2=(root(3)(x)*root(3)(4))/2=(root(3)(4x))/2#.