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

1 Answer
May 30, 2017

Answer:

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)#