Assertion (A) : $(a+ \sqrt{b}) . (a - \sqrt{b})$ is a rational number, where a and b are positive integers. Reason (R) : Product of two irrationals is always rational

Directions : In question below a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option : 

### Assertion (A):
$ (a + \sqrt{b}) \cdot (a - \sqrt{b}) $ is a rational number, where $a$ and $b$ are positive integers.

### Proof:
Using the identity for the difference of squares:

$ (a + \sqrt{b}) \cdot (a - \sqrt{b}) = a^2 - (\sqrt{b})^2 $

$ = a^2 - b $

Since $a$ and $b$ are positive integers, $a^2 - b$ is also an integer, which is a rational number.

Thus, Assertion (A) is **true**.

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### Reason (R):
"Product of two irrationals is always rational."

This statement is **false**. The product of two irrational numbers is **not always** rational. For example:

$ \sqrt{2} \times \sqrt{3} = \sqrt{6} $

which is irrational.

Thus, Reason (R) is **false**.

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### Conclusion:
- Assertion (A) is **true**.
- Reason (R) is **false**.
- Since Reason (R) is incorrect, it does not explain Assertion (A).

**Final Answer:** Assertion is true, but Reason is false.

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