Rationalize the denominator of the expression.

Question

Quizplus · Accepted Answer

To rationalize the denominator, we need to eliminate the square root term on the bottom. We can do this by multiplying both the numerator and denominator by the conjugate of the denominator, which in this case is $\sqrt{b394} + \sqrt{19cef0283364}$. 
\begin{align*}
\frac{11eb12b0_aa84_b61e_b394_d13a071cdf12}{\sqrt{b394} - \sqrt{19cef0283364}} &= \frac{11eb12b0_aa84_b61e_b394_d13a071cdf12 \cdot (\sqrt{b394} + \sqrt{19cef0283364})}{(\sqrt{b394} - \sqrt{19cef0283364}) \cdot (\sqrt{b394} + \sqrt{19cef0283364})} \
&= \frac{11eb12b0_aa84_b61e_b394_d13a071cdf12 \cdot (\sqrt{b394} + \sqrt{19cef0283364})}{b394 - 19cef0283364} \
&= \frac{11eb12b0_aa84_b61e_b394_d13a071cdf12 \cdot (\sqrt{b394} + \sqrt{19cef0283364})}{-19cef0283364 + b394} \
&= \frac{11eb12b0_aa84_b61e_b394_d13a071cdf12 \cdot (\sqrt{b394} + \sqrt{19cef0283364})}{b394 - 19cef0283364} \
&= 11eb12b0_aa84_b621_b394_19cef0283364
\end{align*} 
Therefore, the correct answer is (C).

Rationalize the Denominator of the Expression