Create a problem where the sum of the two numbers is an irrational number.(2 points)

Answer 1

Certainly! Here’s a problem that involves two numbers whose sum is an irrational number:

Problem:
Find two numbers \( x \) and \( y \) such that:

• \( x = \sqrt{2} \)
• \( y = 3 \)

Calculate \( x + y \). Is the result an irrational number?

Solution:
To solve:

1. Calculate \( x + y \): \[ x + y = \sqrt{2} + 3 \]

2. The number \( \sqrt{2} \) is known to be irrational, and adding a rational number (which 3 is) to an irrational number will yield an irrational number.

3. Therefore, the sum \(\sqrt{2} + 3\) is an irrational number.

Conclusion: The sum of the two numbers \( x \) and \( y \) is an irrational number.