3.5 Irrational Numbers — The Numbers That Terrified Ancient Greece | Contemporary Mathematics
After this lesson you will be able to…
- Learn about the ancient Greek Pythagoreans and the shocking discovery of irrational numbers.
- Understand the precise definitions and characteristics of rational and irrational numbers.
- Learn to identify common types of irrational numbers, like non-perfect square roots and Pi.
- Master the technique of simplifying square roots by extracting perfect squares from the radicand.
- Learn the strict rules for adding and subtracting irrational numbers with matching radicands.
- Discover the more flexible rules for multiplying and dividing irrational numbers.
- Learn to rationalize a denominator by multiplying by the irrational term to remove it.
- Master rationalizing complex denominators using the conjugate to eliminate irrational terms.
- Reflect on the Euler-Mascheroni constant and the ongoing discovery of mathematical truths.
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(0)What do a ancient Greek philosophical cult, an infinite decimal, and a mathematical murder legend all have in common? This lesson explores irrational ...
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Quiz: Irrational Numbers — Definitions, Properties, and Operations
FundamentalsAnswer each question based only on what was presented in the video lesson. No outside knowledge is required — every answer can be found in the video.
Practice: Irrational Numbers and Simplifying Square Roots
PracticeApply what you learned in the video about identifying, simplifying, and operating with irrational numbers. Show all work step-by-step; problems increase in difficulty.