How do you rationalize the denominator and simplify #5/(root3(4))#?

2 Answers
Apr 19, 2017

Answer:

#frac{5}{root3 4}=frac{5root3 2}{2}#

Explanation:

Multiply the fraction by #frac{4^(2/3)}{4^(2/3)}#:

#frac{5}{root3 4} color(blue)(xx frac{root3 4}{root3 4} xx frac{root3 4}{root3 4})#

#=frac{5*4^(2/3)}{4}#

#=frac{5root3 16}{4}#

#=frac{5root3(8*2)}{4}#

#=frac{5*2*root3 2}{4}#

#=frac{5root3 2}{2}#

Apr 19, 2017

Answer:

#5/root(3)(4) = (5root(3)(2))/2#

Explanation:

Given:

#5/root(3)(4)#

First note that:

#root(3)(4) = (2^2)^(1/3) = 2^(2/3)#

So to make the denominator rational it will be sufficient to multiply it by #root(3)(2)#...

#5/root(3)(4) = (5root(3)(2))/(root(3)(4)root(3)(2))#

#color(white)(5/root(3)(4)) = (5root(3)(2))/root(3)(4*2)#

#color(white)(5/root(3)(4)) = (5root(3)(2))/root(3)(2^3)#

#color(white)(5/root(3)(4)) = (5root(3)(2))/2#