How do you simplify 2 square root 216 + 4square root 150?

Question

1730 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-28T18:16:30

See a solution process below for:

Simplify #2sqrt(216) + 4sqrt(150)#

First rewrite the terms in radicals as:

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

Next, use this rule for radicals to simplify the radicals:

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

#2sqrt(36)sqrt(6) + 4sqrt(25)sqrt(6) =>#

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

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

Now, we can factor our the common term to complete the simplification:

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

#32sqrt(6)#