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

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Answer 1 · 2018-07-09T22:15:20

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

#\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}#

Answer 2 · 2018-08-03T17:34:37

#root3(5)/4#

#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"#

Answer 3 · 2018-08-03T23:09:49

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

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!