Question

express in simplest radical form.
8√5 − √45

Explanation:

Step1: Simplify \(\sqrt{45}\)

Factor 45: \(45 = 9\times5\), so \(\sqrt{45}=\sqrt{9\times5}\). By the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we get \(\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}\).

Step2: Substitute and simplify

Substitute \(\sqrt{45}=3\sqrt{5}\) into the original expression: \(8\sqrt{5}-3\sqrt{5}\). Combine like terms: \((8 - 3)\sqrt{5}=5\sqrt{5}\).

Answer:

\(5\sqrt{5}\)