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The given expression is \((\sqrt{a} - \sqrt{ac})\), and the problem asks for the product of this expression and its conjugate.

### Step-by-Step Solution:

1. The conjugate of \((\sqrt{a} - \sqrt{ac})\) is \((\sqrt{a} + \sqrt{ac})\).

2. To find the product of an expression and its conjugate, we use the identity:
   \[
   (x - y)(x + y) = x^2 - y^2
   \]
   Here, \(x = \sqrt{a}\) and \(y = \sqrt{ac}\).

3. Applying the identity:
   \[
   (\sqrt{a} - \sqrt{ac})(\sqrt{a} + \sqrt{ac}) = (\sqrt{a})^2 - (\sqrt{ac})^2
   \]

4. Simplify the squares of the square roots:
   \[
   (\sqrt{a})^2 = a \quad \text{and} \quad (\sqrt{ac})^2 = ac
   \]

5. Substituting these into the equation:
   \[
   a - ac
   \]

6. Factor out \(a\):
   \[
   a(1 - c)
   \]

### Final Answer:
The product of \((\sqrt{a} - \sqrt{ac})\) and its conjugate is \(a(1 - c)\).

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Would you like further details or clarification on any step?

### Related Questions:
1. What is the significance of conjugates in simplifying radical expressions?
2. How does the difference of squares formula help in simplifying conjugate products?
3. What are some other common algebraic identities used in simplifying expressions?
4. How would the result change if \(a\) or \(c\) were complex numbers?
5. Can the product of conjugates be used to rationalize denominators? How?

**Tip:** When multiplying a term with its conjugate, the result will always eliminate any square roots or imaginary parts.

Which of the following is the product of (√a − √ac) and its conjugate?

Explore how to find the product of the expression (√a − √ac) and its conjugate using the difference of squares formula. This detailed solution is perfect for students in Grades 9-11, covering key algebraic concepts like radicals and conjugates.

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