## DemiRae 2 years ago Write each expression in lowest terms. Assume that all variables represent positive real numbers:(6p+√24p^3)/3p

1. Decart

$\frac{ 6p+\sqrt{24p ^{3}} }{ 3p }$

2. DemiRae

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?

3. satellite73

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 $\frac{6p+2\sqrt{6p}}{3p}$

4. satellite73

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

5. satellite73

then factor out the common factor of $$p$$ and cancel it with the one in the denominator

6. DemiRae

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