Question

simplify: \\(sqrt{162}\\) \\(\circ\\) 54 \\(\circ\\) \\(81\sqrt{2}\\) \\(\circ\\) \\(9\sqrt{2}\\) \\(\circ\\) 6

Explanation:

Step1: Factor 162

We factor 162 into a product of a perfect square and another number. $$162 = 81\times2$$

Step2: Use square root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 81\) and \(b = 2\)), we get: $$\sqrt{162}=\sqrt{81\times2}=\sqrt{81}\times\sqrt{2}$$

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

Since \(\sqrt{81} = 9\), we have: $$\sqrt{162}=9\sqrt{2}$$

Answer:

\(9\sqrt{2}\) (corresponding to the option with text "9√2")