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Irrational numbers

from class:

Algebra and Trigonometry

Definition

Irrational numbers are real numbers that cannot be expressed as a simple fraction of two integers. They have non-repeating, non-terminating decimal expansions.

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5 Must Know Facts For Your Next Test

  1. The square root of any non-perfect square is an irrational number.
  2. $\pi$ (pi) and $e$ (Euler's number) are classic examples of irrational numbers.
  3. Irrational numbers do not have a repeating or terminating decimal representation.
  4. The sum or product of a rational number and an irrational number is always irrational.
  5. Irrational numbers are part of the real number system but are distinct from rational numbers.

Review Questions

  • Explain why $\sqrt{2}$ is an irrational number.
  • Can the sum of two irrational numbers be rational? Provide an example to support your answer.
  • Is the decimal expansion $3.14159...$ terminating or repeating?
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