Question

question
express in simplest radical form.
\sqrt{162}

Explanation:

Step1: Factor 162 into perfect square and other factor

We know that \(162 = 81\times2\), and \(81 = 9^2\) (a perfect square). So we can rewrite \(\sqrt{162}\) as \(\sqrt{81\times2}\).

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

Applying the property, \(\sqrt{81\times2}=\sqrt{81}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{81}\)

Since \(\sqrt{81} = 9\) (because \(9\times9 = 81\)), we have \(9\times\sqrt{2}\), which is \(9\sqrt{2}\).

Answer:

\(9\sqrt{2}\)