Assertion in reason (a)5 is a rational number
(r) square root of all positive integer is irrational

The question presents a statement with an assertion (A) and a reason (R), which typically requires analyzing whether each of these is true or false and whether the reason correctly explains the assertion.

**Assertion (A):** \(5\) is a rational number.  
This is **true**. A rational number is any number that can be expressed as a fraction \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q \neq 0\). Since \(5\) can be written as \(\frac{5}{1}\), it is a rational number.

**Reason (R):** The square root of all positive integers is irrational.  
This is **false**. The square root of some positive integers is rational (e.g., \(\sqrt{4} = 2\), \(\sqrt{9} = 3\)), while for others, it is irrational (e.g., \(\sqrt{2}\), \(\sqrt{3}\), etc.).

### Conclusion:
- The **assertion (A)** is true, but the **reason (R)** is false.
- Therefore, the reason does not correctly explain the assertion.

Would you like more detailed explanations or have any questions?

Here are 5 related questions to expand on this topic:
1. What are rational and irrational numbers?
2. Can the square root of any non-perfect square be rational?
3. How do you prove that a number is irrational?
4. Why is \( \sqrt{2} \) considered an irrational number?
5. What other examples of rational square roots exist?

**Tip:** A rational number can always be expressed as a ratio of two integers, while an irrational number cannot be written as a fraction.

Assertion in reason (a)5 is a rational number (r) square root of all positive integer is irrational

Explore whether 5 is a rational number and if the square root of all positive integers is irrational. This analysis dives into key mathematical concepts, including rational and irrational numbers, and provides clear reasoning on how to determine the nature of numbers. Suitable for students in Grades 9-10.

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