Question

In the following exercises, simplify.

$\frac{5}{4-\sqrt{11}}$

Short answer

The answer is$4+\sqrt{11}$

Step-by-step solution

Step 1. Given

The expression is$\frac{5}{4-\sqrt{11}}$

Step 2. Rationalize the denominators of the given expressions.

$$\begin{gathered} \frac{5}{4-\sqrt{11}} \\ =\frac{5}{4-\sqrt{11}}\times \frac{4+\sqrt{11}}{4+\sqrt{11}} \\ =\frac{5\left(4+\sqrt{11}\right)}{{\left(4\right)}^2-{\left(\sqrt{11}\right)}^2} \\ =\frac{5\left(4+\sqrt{11}\right)}{16-11} \\ =\frac{5\left(4+\sqrt{11}\right)}{5} \\ =4+\sqrt{11} \end{gathered}$$