How do you simplify #sqrt3(2sqrt5-3sqrt3)#?

1 Answer
Jun 3, 2017

Answer:

Seea solution process below:

Explanation:

First, to eliminate the parenthesis, multiply each term within the parenthesis by the term outside the parenthesis:

#color(red)(sqrt(3))(2sqrt(5) - 3sqrt(3)) =>#

#(color(red)(sqrt(3)) * 2sqrt(5)) - (color(red)(sqrt(3)) * 3sqrt(3)) =>#

#2sqrt(3)sqrt(5) - 3sqrt(3)sqrt(3)#

We can now use this rule for multiplying radicals to simplify the expression:

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

#2sqrt(color(red)(3))sqrt(color(blue)(5)) - 3sqrt(color(red)(3))sqrt(color(blue)(3)) =>#

#2sqrt(color(red)(3) * color(blue)(5)) - 3sqrt(color(red)(3) * color(blue)(3)) =>#

#2sqrt(15) - 3sqrt(9) =>#

#2sqrt(15) - (3 * 3) =>#

#2sqrt(15) - 9#