Question

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

Explanation:

Step1: Factor 54 into prime factors

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

Step2: Apply the square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}(a\geq0,b\geq0)\)

\(\sqrt{54}=\sqrt{3^{2}\times6}\), according to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 3^{2}\), \(b = 6\)), we can get \(\sqrt{3^{2}\times6}=\sqrt{3^{2}}\times\sqrt{6}\).

Step3: Simplify \(\sqrt{3^{2}}\)

Since \(\sqrt{a^{2}}=\vert a\vert\), when \(a = 3\) ( \(3>0\) ), \(\sqrt{3^{2}}=3\). So \(\sqrt{3^{2}}\times\sqrt{6}=3\sqrt{6}\).

Answer:

\(3\sqrt{6}\)