Question

select the correct answer.
what is \\(\sqrt{200}\\) in simplest form?
\\(\bigcirc\\) a. \\(2\sqrt{10}\\)
\\(\bigcirc\\) b. \\(10\sqrt{2}\\)
\\(\bigcirc\\) c. \\(100\sqrt{2}\\)
\\(\bigcirc\\) d. \\(20\sqrt{10}\\)

Explanation:

Step1: Factor 200 into perfect square and other factor

We know that \(200 = 100\times2\), where \(100\) is a perfect square. So, \(\sqrt{200}=\sqrt{100\times2}\).

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

Applying the property, we get \(\sqrt{100\times2}=\sqrt{100}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{100}\)

Since \(\sqrt{100} = 10\), then \(\sqrt{100}\times\sqrt{2}=10\sqrt{2}\).

Answer:

B. \(10\sqrt{2}\)