Question

multiple choice 10 points \\(\sqrt{125}\\) \\(6\sqrt{2}\\) \\(3\sqrt{3}\\) \\(4\sqrt{3}\\) \\(5\sqrt{5}\\)

Explanation:

Step1: Factor 125

We know that \(125 = 25\times5\), and \(25\) is a perfect square. So we can rewrite \(\sqrt{125}\) as \(\sqrt{25\times5}\).

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 \(\sqrt{25\times5}=\sqrt{25}\times\sqrt{5}\).
Since \(\sqrt{25} = 5\), then \(\sqrt{25}\times\sqrt{5}=5\sqrt{5}\).

Answer:

\(5\sqrt{5}\) (assuming the last option is \(5\sqrt{5}\))