Question

express in simplest form with a rational denominator.
\\(\frac{6}{\sqrt{27}}\\)
answer attempt 1 out of 10

Explanation:

Step1: Simplify the square root in the denominator

First, we simplify \(\sqrt{27}\). We know that \(27 = 9\times3\), and \(\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}=3\sqrt{3}\). So the expression becomes \(\frac{6}{3\sqrt{3}}\).

Step2: Simplify the fraction

We can simplify \(\frac{6}{3\sqrt{3}}\) by dividing the numerator and the denominator by 3. So we get \(\frac{2}{\sqrt{3}}\).

Step3: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by \(\sqrt{3}\). So we have \(\frac{2\times\sqrt{3}}{\sqrt{3}\times\sqrt{3}}=\frac{2\sqrt{3}}{3}\) (since \(\sqrt{3}\times\sqrt{3} = 3\)).

Answer:

\(\frac{2\sqrt{3}}{3}\)