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

2 Answers
Anjali G
Apr 19, 2017

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}

George C.
Apr 19, 2017

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

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