Is the sum of a rational number and an irrational number irrational?
Understand the Problem
The question is asking whether adding a rational number (a number that can be expressed as a fraction) to an irrational number (a number that cannot be expressed as a simple fraction) results in an irrational number. The high-level approach to solve this involves understanding the definitions and properties of rational and irrational numbers.
Answer
Irrational
The final answer is that the sum of a rational number and an irrational number is always irrational.
Answer for screen readers
The final answer is that the sum of a rational number and an irrational number is always irrational.
More Information
An interesting aspect of this property is that it holds consistently, no matter which rational or irrational numbers you choose.
Tips
A common mistake is assuming that the sum could sometimes be rational. To avoid this, remember that subtracting a rational number from another cannot yield an irrational number.
Sources
- The web page with info on - Kendall Hunt - im.kendallhunt.com
- How do I prove that the sum of a rational and irrational number is - Math Stack Exchange - math.stackexchange.com
- Operations with Rational and Irrational Numbers - Illustrative Mathematics - tasks.illustrativemathematics.org
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