Question

which expression is equivalent to the given expression? \\(\frac{27}{sqrt{3}}\\) \\(\bigcirc\\) a. \\(sqrt{24}\\) \\(\bigcirc\\) b. \\(9\\) \\(\bigcirc\\) c. \\(\frac{9}{sqrt{3}}\\) \\(\bigcirc\\) d. \\(9sqrt{3}\\) reset selection

Explanation:

Step1: Rationalize the denominator

To simplify \(\frac{27}{\sqrt{3}}\), we multiply the numerator and denominator by \(\sqrt{3}\) to rationalize the denominator.

$$ \frac{27}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} $$

Step2: Simplify the expression

Multiply the numerators and denominators:

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

Then divide 27 by 3:

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

Answer:

D. \(9\sqrt{3}\)