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 \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\))

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

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

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

Answer:

\(5\sqrt{5}\)