Question

How do you add `3sqrt(24) + 2sqrt(54) - 2sqrt(27)`?

Answer 1

`3sqrt(24) + 2sqrt(54) - 2sqrt(27)`

`=3sqrt(4*6) +2sqrt(9*6)-2sqrt(9*3)`

`=3*2sqrt6+2*3sqrt6-2*3sqrt3 = 6sqrt6+6sqrt6-6sqrt3`

`=12sqrt6 - 6sqrt3`

We cannot write these two terms using integers times the same radicand, so we cannot simplify further.