Question

which is \\(\frac{2}{sqrt{3}}\\) simplified?
\\(\frac{2\sqrt{3}}{9}\\)
\\(\frac{\sqrt{6}}{3}\\)
\\(\frac{2\sqrt{3}}{3}\\)
\\(2\sqrt{3}\\)
none of these

Explanation:

Step1: Rationalize the Denominator

To simplify \(\frac{2}{\sqrt{3}}\), we multiply the numerator and the denominator by \(\sqrt{3}\) to rationalize the denominator. This is because \(\sqrt{a}\times\sqrt{a}=a\) for non - negative real numbers \(a\).
So, \(\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\times\sqrt{3}}{\sqrt{3}\times\sqrt{3}}\)

Step2: Simplify the Denominator

We know that \(\sqrt{3}\times\sqrt{3} = 3\) (by the property \(\sqrt{a}\times\sqrt{a}=a\) where \(a = 3\)). So the expression becomes \(\frac{2\sqrt{3}}{3}\)

Answer:

\(\frac{2\sqrt{3}}{3}\) (corresponding to the option with \(\frac{2\sqrt{3}}{3}\))