Question

is square root of rpi squared irrational or rational
is 9pi irrational or rational
adding them together is irrational or rational

Answer 1

Let's analyze each part of your question step by step:

1. **Square root of π²:**
- The square root of π² is |π| (the absolute value of π).
- Since π is an irrational number, |π| is also irrational.
- Therefore, the square root of π² is irrational.

2. **9π:**
- Here, 9 is a rational number and π is an irrational number.
- The product of a rational number (9) and an irrational number (π) is irrational.
- Thus, 9π is irrational.

3. **Adding them together (√(π²) + 9π):**
- We have |π| (irrational) + 9π (irrational).
- The sum of two irrational numbers is not guaranteed to be irrational. It can be either rational or irrational depending on the specific numbers involved.
- In this case, |π| (which equals π) and 9π are both irrational, but their sum (π + 9π) simplifies to 10π.
- Since 10π is the product of an integer (10) and an irrational number (π), it is irrational.

**Conclusion:**
- The square root of π² is irrational.
- 9π is irrational.
- Their sum, |π| + 9π (which is 10π), is also irrational.