Question

How do you simplify `-sqrt12+3sqrt3`?

Answer 1

See a solution process below:

Explanation:

We can use this rule of radicals to rewrite the radical on the left of the expression:

`sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))`

`-sqrt(12) + 3sqrt(3) => -sqrt(4 * 3) + 3sqrt(3) => -(sqrt(4) * sqrt(3)) + 3sqrt(3) => -2sqrt(3) + 3sqrt(3)`

We can now combine like terms. In this case the `sqrt(3)` term is the like term:

`-2sqrt(3) + 3sqrt(3) => (-2 + 3)sqrt(3) => -1sqrt(3) =>`

`-sqrt(3)`