Question

express in simplest radical form. \\(\sqrt{108}\\)

Explanation:

Step1: Factor 108 into perfect square and other factor

We know that \(108 = 36\times3\), where 36 is a perfect square (\(36 = 6^2\)). So we can rewrite \(\sqrt{108}\) as \(\sqrt{36\times3}\).

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

Applying the property, we get \(\sqrt{36\times3}=\sqrt{36}\times\sqrt{3}\).

Step3: Simplify \(\sqrt{36}\)

Since \(\sqrt{36} = 6\) (because \(6^2=36\)), we substitute this value in. So \(\sqrt{36}\times\sqrt{3}=6\sqrt{3}\).

Answer:

\(6\sqrt{3}\)