Question

How do you simplify `2 sqrt(3) *times* (5 sqrt(2) + 5 sqrt(5))`?

Answer 1

`2sqrt(3)(5sqrt(2)+5sqrt(5))=10sqrt(6)+10sqrt(15)`

Explanation:

You cannot add unlike square roots, but you can multiply them. The only thing to do here is to distribute `2sqrt(3)` to the two terms inside the parentheses. So `2sqrt(3)*5sqrt(2)=(2*5)(sqrt(3*2))=10sqrt(6)`
Likewise, `2sqrt(3)*5sqrt(5)=(2*5)(sqrt(3*5))=10sqrt(15)`
Add these together, and
`2sqrt(3)(5sqrt(2)+5sqrt(5))=10sqrt(6)+10sqrt(15)`
Because neither of the numbers under the radicals in the answer have a perfect square as a multiple, this is the simplest answer you can get.