Question

1.2 knowledge check
started: feb 3 at 10:42am
quiz instructions
question 1
simplify: \\(\sqrt{243}\\)
\\(\circ\\) 9
\\(\circ\\) \\(81\sqrt{2}\\)
\\(\circ\\) 81
\\(\circ\\) \\(9\sqrt{3}\\)

Explanation:

Step1: Factor 243

We know that \(243 = 81\times3\), since \(81\times3 = 243\).

Step2: Use square - root property

According to the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{243}=\sqrt{81\times3}=\sqrt{81}\times\sqrt{3}\).

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

Since \(9\times9 = 81\), then \(\sqrt{81}=9\). So \(\sqrt{81}\times\sqrt{3}=9\sqrt{3}\).

Answer:

\(9\sqrt{3}\) (corresponding to the option \(9\sqrt{3}\))