Question

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

Explanation:

Step1: Factor 200

We know that \(200 = 100\times2\), so \(\sqrt{200}=\sqrt{100\times2}\).

Step2: Use square - root property

According to the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{100\times2}=\sqrt{100}\times\sqrt{2}\).
Since \(\sqrt{100} = 10\), then \(\sqrt{100}\times\sqrt{2}=10\sqrt{2}\).

Answer:

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