Question

which expression is equivalent to \\(\sqrt{120x}\\)?
\\(2\sqrt{30x}\\)
\\(2\sqrt{30}\\)
\\(4\sqrt{30x}\\)
\\(60\sqrt{2x}\\)

Explanation:

Step1: Factor 120x

Factor 120x into prime factors: \(120x = 4\times30x\), where 4 is a perfect square.

Step2: Apply square root property

Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (for \(a\geq0,b\geq0\)), we have \(\sqrt{120x}=\sqrt{4\times30x}=\sqrt{4}\cdot\sqrt{30x}\).
Since \(\sqrt{4} = 2\), this simplifies to \(2\sqrt{30x}\).

Answer:

\(2\sqrt{30x}\) (the first option)