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.

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