How do you simplify #3sqrt( (27 + 1 ))#?

1 Answer
Mar 11, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite the expression within the radical as:

#3sqrt(27 + 1) => 3sqrt(28) => 3sqrt(4 * 7)#

Now, use this rule for radicals to simplify the radical:

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

#3sqrt(color(red)(4) * color(blue)(7)) =>#

#3sqrt(color(red)(4)) * sqrt(color(blue)(7)) =>#

#3 * 2 * sqrt(color(blue)(7)) =>#

#6sqrt(color(blue)(7))#