Question

Rationalize the denominator.
11/ squareroot 17 - 4

11/ squareroot 17 - 4
(Please simplify your answer. Type an exact answer, using radicals as needed.)

Answer 1

To rationalize the denominator of the expression \(\frac{11}{\sqrt{17} - 4}\), we can multiply the numerator and denominator by the conjugate of the denominator, which is \(\sqrt{17} + 4\).

Here are the steps:

1. Write the expression:
\[
\frac{11}{\sqrt{17} - 4}
\]

2. Multiply the numerator and the denominator by the conjugate of the denominator:
\[
\frac{11(\sqrt{17} + 4)}{(\sqrt{17} - 4)(\sqrt{17} + 4)}
\]

3. Simplify the denominator using the difference of squares:
\[
(\sqrt{17})^2 - (4)^2 = 17 - 16 = 1
\]

4. Now, rewrite the expression:
\[
\frac{11(\sqrt{17} + 4)}{1} = 11(\sqrt{17} + 4) = 11\sqrt{17} + 44
\]

Thus, the rationalized form of \(\frac{11}{\sqrt{17} - 4}\) is:
\[
11\sqrt{17} + 44
\]