Question

question
express in simplest radical form.
\sqrt{108}

Explanation:

Step1: Factor 108 into perfect squares and others

We know that \(108 = 36\times3\), where 36 is a perfect square. 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 \(\sqrt{36} = 6\), we substitute it back to get \(6\times\sqrt{3}=6\sqrt{3}\).

Answer:

\(6\sqrt{3}\)