Question

$\sqrt{x^5} =$

Explanation:

Step1: Rewrite the radicand

Rewrite \(x^5\) as \(x^4\cdot x\), so \(\sqrt{x^5}=\sqrt{x^4\cdot x}\).

Step2: Apply the square - root property

According to the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{x^4\cdot x}=\sqrt{x^4}\cdot\sqrt{x}\).
Since \(\sqrt{x^4} = x^2\) (because \((x^2)^2=x^4\) and \(x^2\geq0\) for real - valued \(x\) in the domain of the square root), then \(\sqrt{x^4}\cdot\sqrt{x}=x^2\sqrt{x}\).

Answer:

\(x^{2}\sqrt{x}\)