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

Question

1278 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-11T21:59:20

See a solution process below:

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))#