How do you simplify root3(5/64)?

3 Answers

1/2\root[5]{5/2}

Explanation:

\root[5]{5/64}

=\root[5]{5/{2\cdot 2^5}}

=\root[5]{(5/{2})(1/2^5)}

=\root[5]{5/2}\root[5]{1/2^5}

=\root[5]{5/2}1/\root[5]{2^5}

=\root[5]{5/2}\cdot 1/2

=1/2\root[5]{5/2}

Aug 3, 2018

root3(5)/4

Explanation:

root3(5/64)

:.=root3(5)/(root3(64))

:.=root3(5)/(root3(2*2*2*2*2*2))

:.=root3(a)*root3(a)*root3(a)=a

:.=root3(5)/4

~~~~~~~~~~~~

:.root3(5/64)=0.427493986"by calculator"

:.root 3(5)/4=0.427493986"by calculator"

Aug 3, 2018

root3(5)/4, or 5^(1/3)/4

Explanation:

We can rewrite this as

root3(5)/root3(64)

Since 5 isn't a perfect cube, we cannot simplify the numerator further, but recall that

4^3=64. With this in mind, root3(64) simplifies to 4, and we're left with

root3(5)/4, which can be alternatively written as 5^(1/3)/4.

Hope this helps!