Question

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

Answer 1

`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)`