Question

express in simplest radical form.\\(\sqrt{180}\\)

Explanation:

Step1: Factor 180 into perfect square and other factor

We know that \(180 = 36\times5\), where 36 is a perfect square (\(36 = 6^2\)). So we can rewrite \(\sqrt{180}\) as \(\sqrt{36\times5}\).

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

Applying the property, \(\sqrt{36\times5}=\sqrt{36}\times\sqrt{5}\). Since \(\sqrt{36} = 6\), we get \(6\times\sqrt{5}=6\sqrt{5}\).

Answer:

\(6\sqrt{5}\)