4√3- 6√54√3- 6√5
`4sqrt3 - 6sqrt5`
The radicand 3 and 5 are already in their prime numbers which indicates that there is no number when multiplied by itself equals to 3 or 5. So we could no longer simplify `sqrt 3` and `sqrt5` .
Also, to subtract radicals, the radicand and the index of the radical should be the same.
For example if we have `11sqrt7 - 2sqrt7` , since both terms have the same radicand and index which is `sqrt7` , we can subtract the two terms. And its difference is `11sqrt7-2sqrt7 = (11-2)=9sqrt7` .
In the problem above, the two terms do not have the same radicand.
Hence, we can not subtract the two terms. So its simplified form is still the same which is `4sqrt3-6sqrt5` .