Question

Rationalize the denominator.

11/squareroot5-2

11/squareroot5-2= blank

Answer 1

To rationalize the denominator of the expression \(\frac{11}{\sqrt{5} - 2}\), we can multiply the numerator and the denominator by the conjugate of the denominator, which is \(\sqrt{5} + 2\).

Here’s how we do it step by step:

\[
\frac{11}{\sqrt{5} - 2} \cdot \frac{\sqrt{5} + 2}{\sqrt{5} + 2} = \frac{11(\sqrt{5} + 2)}{(\sqrt{5} - 2)(\sqrt{5} + 2)}
\]

Now, simplify the denominator:

\[
(\sqrt{5} - 2)(\sqrt{5} + 2) = \sqrt{5}^2 - 2^2 = 5 - 4 = 1
\]

Now substituting back, we have:

\[
\frac{11(\sqrt{5} + 2)}{1} = 11(\sqrt{5} + 2)
\]

Thus, the rationalized form of the expression is:

\[
11\sqrt{5} + 22
\]

So, the final answer is:

\[
\frac{11}{\sqrt{5} - 2} = 11\sqrt{5} + 22
\]