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lemjay eNotes educator| Certified Educator

`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` .