Question

a radical expression is shown.
\\(\sqrt{72x^2y}\\)
which is an equivalent expression?
\\(\bigcirc\\) a \\(6x\sqrt{2y}\\)
\\(\bigcirc\\) b \\(6y\sqrt{2x}\\)
\\(\bigcirc\\) c \\(36x\sqrt{2y}\\)
\\(\bigcirc\\) d \\(36y\sqrt{2x}\\)

Explanation:

Step1: Factor the radicand

Factor \(72x^2y\) into perfect squares and remaining factors: \(72x^2y = 36x^2 \cdot 2y\)

Step2: Apply square root property

Use \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\)): \(\sqrt{36x^2 \cdot 2y}=\sqrt{36x^2}\cdot\sqrt{2y}\)

Step3: Simplify the perfect square root

Simplify \(\sqrt{36x^2}\): \(\sqrt{36x^2} = 6x\) (since \(x^2\) square root is \(|x|\), assuming \(x\geq0\) for simplicity here)

Step4: Combine the results

Combine to get \(6x\sqrt{2y}\)

Answer:

A. \(6x\sqrt{2y}\)