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To rationalize the denominator of \(\frac{10}{4 + \sqrt{6}}\), we need to eliminate the square root in the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is \(4 - \sqrt{6}\).

### Step-by-Step Solution:

1. **Multiply the numerator and the denominator by \(4 - \sqrt{6}\):**

   \[
   \frac{10}{4 + \sqrt{6}} \times \frac{4 - \sqrt{6}}{4 - \sqrt{6}} = \frac{10(4 - \sqrt{6})}{(4 + \sqrt{6})(4 - \sqrt{6})}
   \]

2. **Simplify the denominator using the difference of squares formula:**

   \[
   (4 + \sqrt{6})(4 - \sqrt{6}) = 4^2 - (\sqrt{6})^2 = 16 - 6 = 10
   \]

   So, the expression becomes:

   \[
   \frac{10(4 - \sqrt{6})}{10}
   \]

3. **Cancel out the \(10\) in the numerator and the denominator:**

   \[
   = 4 - \sqrt{6}
   \]

### Final Answer:
The rationalized form is:
\[
4 - \sqrt{6}
\]

Would you like more details on any specific part of the solution?

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Here are 5 related questions that might deepen your understanding:

1. How does the difference of squares help in rationalizing denominators?
2. What is the purpose of multiplying by the conjugate?
3. How can you verify that a denominator has been fully rationalized?
4. How would you rationalize a denominator with both a square root and a cube root?
5. What are some common mistakes to watch for when rationalizing complex denominators?

**Tip:** When rationalizing, always simplify the final expression to check if terms can be further reduced.

Rationalise the denominator of 10 / (4 + √6) giving your answer in its simplest form.

Learn how to rationalize the denominator of 10 / (4 + √6) with a step-by-step solution. This solution covers concepts in rationalization and the difference of squares, ideal for Grades 9-10.

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