Question

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

Answer 1

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.