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

1 Answer
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.