Question

How do you simplify `sqrt2(sqrt6+sqrt8)+sqrt3`?

Answer 1

We are going to expand :

`=sqrt2*sqrt6+sqrt2*sqrt8+sqrt3`
`=sqrt12+sqrt16+sqrt3`
`=sqrt(4*3)+4+sqrt3` ( since `sqrt16=4` )
`=sqrt4*sqrt3+4+sqrt3`
`=2sqrt3+4+sqrt3` ( since `sqrt4=2` )
`=3sqrt3+4`