Question

How do you simplify `sqrt2(sqrt6+sqrt10)`?

Answer 1

Radicals can be multiplied together as long as they are all under the same "root" , like square roots, cube roots, or other roots.

Explanation:

I would expand by Distributing:
`sqrt(2)*sqrt(6) + sqrt(2)*sqrt(10)`
= `sqrt(2)sqrt(2)sqrt(3) + sqrt(2)sqrt(2)sqrt(5)`
and look for "pairs" of matching roots.
=`sqrt(2^2)sqrt(3)+sqrt(2^2)sqrt(5)` (you could even skip this step)
= `2sqrt(3) + 2sqrt(5)`.

Pairs of roots that are the same factor simplify easily:
`sqrt(93)sqrt(93) = 93` every time!!