Question

station 1 simplifying radicals ma simplify the following radical: \\(sqrt{288}\\) \\(7sqrt{2}\\) \\(12sqrt{2}\\) \\(12sqrt{5}\\) \\(6sqrt{2}\\) \\(6sqrt{5}\\) \\(5sqrt{2}\\)

Explanation:

Step1: Factor 288 into perfect square and other

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

Step2: Use radical property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\)

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 144\) and \(b = 2\)), we get \(\sqrt{144\times2}=\sqrt{144}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{144}\)

Since \(\sqrt{144} = 12\) (because \(12\times12 = 144\)), then \(\sqrt{144}\times\sqrt{2}=12\sqrt{2}\).

Answer:

\(12\sqrt{2}\) (corresponding to the option: \(12\sqrt{2}\))