Question

simplify. assume v is greater than or equal to zero. \\(\sqrt{12v^{6}}\\)

Explanation:

Step1: Factor the radicand

We can factor \(12v^6\) as \(4\times3\times v^6\). Since \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (for \(a\geq0,b\geq0\)), we can rewrite \(\sqrt{12v^6}\) as \(\sqrt{4\times3\times v^6}\).

Step2: Simplify each square root

We know that \(\sqrt{4} = 2\) and \(\sqrt{v^6}=v^3\) (because \(v\geq0\), so we don't need to consider the absolute value). Then \(\sqrt{4\times3\times v^6}=\sqrt{4}\cdot\sqrt{3}\cdot\sqrt{v^6}=2\times\sqrt{3}\times v^3\).

Step3: Combine the terms

Combining the terms, we get \(2v^3\sqrt{3}\).

Answer:

\(2v^{3}\sqrt{3}\)