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

1 Answer
lechugamaestro19
Feb 22, 2018

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)

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