Question

question
express in simplest radical form.
\sqrt{162}
answer attempt 1 out of 2

Explanation:

Step1: Factor 162

Find the largest perfect square factor of 162. We know that \(162 = 81\times2\), where 81 is a perfect square (\(9^2 = 81\)).

Step2: Apply square root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we have \(\sqrt{162}=\sqrt{81\times2}=\sqrt{81}\times\sqrt{2}\).
Since \(\sqrt{81} = 9\), this simplifies to \(9\sqrt{2}\).

Answer:

\(9\sqrt{2}\)