How do you simplify #2 sqrt216 + 4sqrt 150#?

1 Answer
Jul 9, 2017

Answer:

See a solution process below:

Explanation:

First, we can rewrite the terms within the radicals as:

#2sqrt(36 * 6) + 4sqrt(25 * 6)#

We can use this rule of radicals to simplify the radical terms:

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

#2sqrt(color(red)(36) * color(blue)(6)) + 4sqrt(color(red)(25) * color(blue)(6)) => 2sqrt(color(red)(36))sqrt(color(blue)(6)) + 4sqrt(color(red)(25))sqrt(color(blue)(6)) =>#

#(2 * 6sqrt(6)) + (4 * 5sqrt(6)) => 12sqrt(6) + 20sqrt(6)#

We can now combine like terms:

#12sqrt(6) + 20sqrt(6) => (12 + 20)sqrt(6) =>#

#32sqrt(6)#