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Let's begin by simplifying the given expression:

\[
\frac{(4 - \sqrt{5})(4 + \sqrt{5})}{2\sqrt{11}}
\]

This involves simplifying the numerator using the difference of squares:

\[
(4 - \sqrt{5})(4 + \sqrt{5}) = 4^2 - (\sqrt{5})^2 = 16 - 5 = 11
\]

Thus, the expression becomes:

\[
\frac{11}{2\sqrt{11}}
\]

Now, we can simplify this expression further by dividing both the numerator and denominator by \(\sqrt{11}\):

\[
\frac{11}{2\sqrt{11}} = \frac{11}{2} \cdot \frac{1}{\sqrt{11}} = \frac{11}{2\sqrt{11}} = \frac{\sqrt{11}}{2}
\]

Now we can see that the expression is in the form:

\[
\frac{\sqrt{a}}{b}
\]

where \( a = 11 \) and \( b = 2 \).

Thus, the values of \(a\) and \(b\) are:

\[
a = 11, \quad b = 2
\]

Would you like a deeper explanation on any step? Here are five related questions to expand your understanding:

1. How does the difference of squares formula apply to algebraic expressions?
2. Can we generalize this process for expressions with other surds?
3. Why is rationalizing the denominator important in some mathematical contexts?
4. What are some common properties of square roots that simplify expressions?
5. How does simplifying radical expressions differ when coefficients are involved?

**Tip:** When simplifying expressions involving square roots, always check if applying the difference of squares helps to reduce the complexity quickly.

Write (4 - √5)(4 + √5) / (2√11) in the form √a / b, where a and b are integers. Find the values of a and b.

Learn how to simplify the expression (4 - √5)(4 + √5) / (2√11) and rewrite it in the form √a / b. This problem covers algebraic concepts like the difference of squares and radical simplification, suitable for students in Grades 9-11.

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