If you add a rational number, such as 5, to an irrational number, such as , the result is _________.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's understanding of the properties of irrational numbers, specifically the closure property under addition with a rational number.
Key Concept Explanation
The sum of a rational number and an irrational number is always irrational. This is because adding a rational number to an irrational number does not change the non-terminating, non-repeating nature of the irrational number.
Step-by-step Solution
1. Consider the rational number 5 and the irrational number .
2. Add the two numbers: 5 +
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