Question
Explain why the sum of a rational number and an irrational number must be irrational.
Step 1
A rational number can be expressed as a fraction, i.e., a/b, where a and b are integers and b ≠ 0. Show more…
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Key Concepts
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Explain why the sum, the difference, and the product of two rational numbers are rational numbers. Is the product of two irrational numbers necessarily irrational? What about the sum?
Prerequisites
Real Numbers and Their Properties
Explain why the sum and product of two rational numbers are always rational.
Basics
Number Systems
In your own words, explain why every irrational number is a real number but not every real number is an irrational number.
Real Number and Algebraic Expressions
Algebraic Expressions and Sets of Numbers
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