Question

simplify.
\sqrt{45}

Explanation:

Step1: Factor 45 into prime factors

We know that \(45 = 9\times5\), and \(9 = 3^2\). So we can rewrite \(\sqrt{45}\) as \(\sqrt{9\times5}\).

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

Applying this property, we get \(\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}\).

Step3: Simplify \(\sqrt{9}\)

Since \(3^2 = 9\), \(\sqrt{9}=3\). So the expression becomes \(3\sqrt{5}\).

Answer:

\(3\sqrt{5}\)