Question

express the given radical in simplest form: \\(\sqrt{288}\\)\
\\(\bigcirc\\) a. \\(12\sqrt{2}\\)\
\\(\bigcirc\\) b. \\(36\sqrt{8}\\)\
\\(\bigcirc\\) c. \\(48\sqrt{6}\\)\
\\(\bigcirc\\) d. \\(96\sqrt{3}\\)\
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Explanation:

Step1: Factor 288 into perfect square and other factor

We know that \(288 = 144\times2\), where \(144\) is a perfect square (\(12^2 = 144\)). So we can rewrite \(\sqrt{288}\) as \(\sqrt{144\times2}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

Applying the property, \(\sqrt{144\times2}=\sqrt{144}\times\sqrt{2}\). Since \(\sqrt{144} = 12\), we get \(12\sqrt{2}\).

Answer:

A. \(12\sqrt{2}\)