How do you simplify #root5(6)+5root5(6)#?

1 Answer
Tom Kiefer
Jul 19, 2016

Start by noticing a chance to use the Distributive Property lurking in there, and them just combine terms.

Explanation:

#root(5)(6) + 5root(5)(6)#
#=1root(5)(6) + 5root(5)(6)# ← 'cause 1 times anything is still just as anything
#=(1+5)root(5)(6)# ← distributive property applied
#=6root(5)(6)#
#=6*6^(1/5)#
#=6^1*6^(1/5)#
#=6^(6/5)=6^1.2#

If that radical is itself a bit noisy to look at, and you happen to notice that it's exactly the same radical in two places, try replacing that noisy #root(5)(6)# with #x# first and see if the distributive property usage becomes more obvious, then plug the #root(5)(6)# back in and keep going.

IAC, whether and how far you take it past that depends on what "simplify" means to you at the moment.

Related questions
See all questions in Addition and Subtraction of Radicals
Impact of this question
2071 views around the world
You can reuse this answer
Creative Commons License