INSTRUCTION: From the words lettered A-D choose the appropriate answer
Rationalize \(\frac{3}{9-\sqrt{80}}\)
A. \(3(9+\sqrt{80}\)
B. \(3 / 161(9-\) \(\sqrt{80}\)
C. \(3(9-\sqrt{80})\)
D. \(3 / 161(9+\sqrt{80})\)
Correct Answer: A
Explanation
\begin{array}{l}
\text { To rationalize } \frac{3}{9-\sqrt{80}} \\
\Rightarrow \frac{3}{9-\sqrt{80}} \times \frac{3+\sqrt{80}}{9+\sqrt{80}} \\
=\frac{3(9+\sqrt{80})}{(9-\sqrt{80})(9+\sqrt{80})} \\
=\frac{27+3 \sqrt{80}}{81-80} \\
=27+3 \sqrt{80} \\
=(9+\sqrt{80})
\end{array}
