Question

How do you add `sqrt12+sqrt75`?

Answer 1

If you take the number apart (factorize) you'll see that:
`12=2*2*3and75=3*5*5`

Explanation:

You can take the 'doubles' (squares) out from under the root, where they become single:

`sqrt12=sqrt(2*2*3)=sqrt(2^2)*sqrt3=2sqrt3`

`sqrt75=sqrt(5*5*3)=sqrt(5^2)*sqrt3=5sqrt3`

Adding these will give you `7sqrt3` as the final answer.