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

2 Answers
Apr 15, 2017

root3(x/2)

Explanation:

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

Apr 15, 2017

(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.