Question

which expression is equivalent to \\(\sqrt{200}\\)?
\\(\circ\\) \\(2\sqrt{10}\\)
\\(\circ\\) \\(10\sqrt{2}\\)
\\(\circ\\) \\(10\sqrt{20}\\)
\\(\circ\\) \\(100\sqrt{2}\\)

Explanation:

Step1: Factor 200 into perfect square and other

We know that \(200 = 100\times2\), where 100 is a perfect square (\(10^2\)). So, \(\sqrt{200}=\sqrt{100\times2}\).

Step2: Use square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

According to the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 100,b = 2\) here), we have \(\sqrt{100\times2}=\sqrt{100}\times\sqrt{2}\).
Since \(\sqrt{100} = 10\) (because \(10\times10=100\)), then \(\sqrt{100}\times\sqrt{2}=10\sqrt{2}\).

Answer:

\(10\sqrt{2}\) (the option with \(10\sqrt{2}\))