How do you simplify #root3(5/64)#?

3 Answers

Answer:

#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

Answer:

#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

Answer:

#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!