How do you simplify # sqrt108 + 5sqrt3#?

1 Answer
Mar 6, 2018

Answer:

See a solution process below:

Explanation:

First we can rewrite the radical on the left as:

#sqrt(36 * 3) + 5sqrt(3)#

We can then use this rule for radicals to simplify the radical on the left:

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

#sqrt(color(red)(36) * color(blue)(3)) + 5sqrt(3) =>#

#(sqrt(color(red)(36)) * sqrt(color(blue)(3))) + 5sqrt(3) =>#

#6sqrt(3) + 5sqrt(3)#

We can now factor the common term and complete the simplification:

#(6 + 5)sqrt(3) =>#

#11sqrt(3)#