\(Use:\\\sqrt{a^2}=a\\\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\a^{n+m}=a^n\cdot a^m\\==============================\\\sqrt{80p^3}=\sqrt{16\cdot5p^{2+1}}=\sqrt{4^2\cdot5\cdot p^2\cdot p}=\sqrt{4^2p^2\cdot5p}\\\\=\sqrt{4^2p^2}\cdot\sqrt{5p}=\sqrt{4^2}\cdot\sqrt{p^2}\cdot\sqrt{5p}=4\cdot p\cdot\sqrt{5p}\\\\=\boxed{4p\sqrt{5p}}\)