Question

Write each expression in lowest terms. Assume that all variables represent positive real numbers:(6p+√24p^3)/3p

Answer 1

\[\frac{ 6p+\sqrt{24p ^{3}} }{ 3p }\]

Answer 2

That is how it is set up, it says I'm suppose to factor the numerator and denominator. The denominator ends up being 3 alone and the numerator looks like: 6+2√6p in the answer key, so the two p's must cancel on top and bottom, but where does the cube go?

Answer 3

since \(\sqrt{24}=\sqrt{4\times 6}=\sqrt{4}\sqrt{6}=2\sqrt{6}\) and \(\sqrt{p^3}=p\sqrt{p}\) you can start with
\[\frac{6p+2\sqrt{6p}}{3p}\]

Answer 4

oops i meant start with
\[\frac{6p+2p\sqrt{6p}}{3p}\]

Answer 5

then factor out the common factor of \(p\) and cancel it with the one in the denominator

Answer 6

Thank you! I appreciate your help! I see how it is done now.