Question

How do you simplify `2sqrt3-sqrt27`?

Answer 1

`-sqrt3`

Explanation:

We can see if the numbers in the square roots can be simplified with factoring.
`2sqrt(3) - sqrt(27)`

We know that 3 is prime, so it cannot be simplified. 27 can be factored
`27 = 3^3 = 3^2 cdot 3`

which means
`2sqrt(3) - sqrt(3^2 * 3) = 2sqrt3 - sqrt(3^2) sqrt(3) = 2sqrt3 - 3sqrt3 = -sqrt3`