How do you simplify 3sqrt(5c) times sqrt15^335c×153?

1 Answer
Feb 22, 2018

225sqrt(3c)2253c

Explanation:

3sqrt(5c)sqrt(15)^335c153

First, we can simplify sqrt(15)^3153.
sqrt(15)^3 = sqrt15*sqrt15*sqrt15 = 15*sqrt15153=151515=1515
3*15sqrt(5c)sqrt153155c15
45sqrt(5c)sqrt15455c15

Then, we can consolidate and simplify our two irrationals.
sqrt(alpha)*sqrt(beta) = sqrt(alphabeta)αβ=αβ
sqrt(5c)sqrt15 = sqrt(75c)5c15=75c
45sqrt(75c)4575c
sqrt(75c) = sqrt25sqrt(3c)75c=253c
45*5sqrt(3c)4553c

This brings us to a simplification of the original statement:
225sqrt(3c)2253c