Question

create 5 problems where the sum of two numbers is an irrational number

Answer 1

Sure! Here are five problems where the sum of two numbers results in an irrational number:

1. **Problem 1:**
Calculate the sum of \( \sqrt{2} \) and \( 3 \).
- Solution: \( \sqrt{2} + 3 \) is irrational.

2. **Problem 2:**
What is the result of adding \( \pi \) and \( -\pi + 1 \)?
- Solution: \( \pi + (-\pi + 1) = 1 \), which is rational. Therefore, let's adjust this:
Calculate \( \pi + 2 \).
- Solution: \( \pi + 2 \) is irrational.

3. **Problem 3:**
Find the sum of \( \sqrt{3} \) and \( \sqrt{3} \).
- Solution: \( \sqrt{3} + \sqrt{3} = 2\sqrt{3} \), which is irrational.

4. **Problem 4:**
What is the sum of \( \sqrt{5} \) and \( -\sqrt{5} + 4 \)?
- Solution: \( \sqrt{5} + (-\sqrt{5} + 4) = 4 \), which is rational. To modify: Calculate \( \sqrt{5} + 1 \).
- Solution: \( \sqrt{5} + 1 \) is irrational.

5. **Problem 5:**
Find the sum of \( 7 \) and \( \sqrt{7} \).
- Solution: \( 7 + \sqrt{7} \) is irrational.

Each of these problems involves the sum of numbers that yields an irrational result!