Question

question
express in simplest radical form.
\\(\sqrt{54}\\)

Explanation:

Step1: Factor 54 into prime factors

We know that \(54 = 9\times6\), and \(9 = 3^2\), \(6=2\times3\). So \(54 = 3^2\times6\).

Step2: Apply square - root property

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{54}=\sqrt{3^{2}\times6}\).
Then, by the property \(\sqrt{a^{2}} = a\) (\(a\geq0\)), \(\sqrt{3^{2}\times6}=\sqrt{3^{2}}\times\sqrt{6}\).
Since \(\sqrt{3^{2}} = 3\), we get \(3\sqrt{6}\).

Answer:

\(3\sqrt{6}\)