Question

simplify.
\sqrt{125}

Explanation:

Step1: Factor 125 into prime factors

We know that \(125 = 5\times5\times5 = 5^{2}\times5\).

Step2: Simplify the square root

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we have \(\sqrt{125}=\sqrt{5^{2}\times5}\).
According to the property \(\sqrt{a^{2}} = a\) (for \(a\geq0\)), \(\sqrt{5^{2}\times5}=\sqrt{5^{2}}\times\sqrt{5}=5\sqrt{5}\).

Answer:

\(5\sqrt{5}\)