Question

simplify.
\sqrt{125}

Explanation:

Step1: Factor 125 into prime factors

We know that \(125 = 25\times5\), and \(25 = 5^2\), so \(125=5^2\times5\).

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

\(\sqrt{125}=\sqrt{5^2\times5}=\sqrt{5^2}\times\sqrt{5}\)

Step3: Simplify \(\sqrt{5^2}\)

Since \(\sqrt{a^2}=a\) for \(a\geq0\), then \(\sqrt{5^2} = 5\). So \(\sqrt{125}=5\sqrt{5}\)

Answer:

\(5\sqrt{5}\)