Question

which is the simplest form of \\(\frac{7}{\sqrt{27}}\\)?
options: (21sqrt{3}), (7sqrt{27}), (\frac{7sqrt{3}}{9}), (\frac{7sqrt{27}}{27})

Explanation:

Step1: Simplify the denominator

$\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$

Step2: Rationalize the fraction

$\frac{7}{3\sqrt{3}} = \frac{7 \times \sqrt{3}}{3\sqrt{3} \times \sqrt{3}} = \frac{7\sqrt{3}}{3 \times 3}$

Step3: Simplify the denominator

$\frac{7\sqrt{3}}{9}$

Answer:

C. $\frac{7\sqrt{3}}{9}$