Question

simplify √(72p⁷). the simplified expression is

Explanation:

Step1: Factor the radicand

Factor \(72p^7\) into perfect squares and remaining factors. \(72 = 36\times2\) and \(p^7 = p^6\times p\). So, \(\sqrt{72p^7}=\sqrt{36\times2\times p^6\times p}\).

Step2: Apply square root properties

Use the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)) and \(\sqrt{a^2}=a\) (\(a\geq0\)). We get \(\sqrt{36}\times\sqrt{p^6}\times\sqrt{2p}\). Since \(\sqrt{36} = 6\) and \(\sqrt{p^6}=p^3\) (because \((p^3)^2=p^6\)), the expression simplifies to \(6p^3\sqrt{2p}\).

Answer:

\(6p^3\sqrt{2p}\)