How do you simplify #3sqrt(5c) times sqrt15^3#?

1 Answer
Feb 22, 2018

Answer:

#225sqrt(3c)#

Explanation:

#3sqrt(5c)sqrt(15)^3#

First, we can simplify #sqrt(15)^3#.
#sqrt(15)^3 = sqrt15*sqrt15*sqrt15 = 15*sqrt15#
#3*15sqrt(5c)sqrt15#
#45sqrt(5c)sqrt15#

Then, we can consolidate and simplify our two irrationals.
#sqrt(alpha)*sqrt(beta) = sqrt(alphabeta)#
#sqrt(5c)sqrt15 = sqrt(75c)#
#45sqrt(75c)#
#sqrt(75c) = sqrt25sqrt(3c)#
#45*5sqrt(3c)#

This brings us to a simplification of the original statement:
#225sqrt(3c)#