Podcast Beta
Questions and Answers
What can be concluded when there exist co-prime positive integers a and b such that an algebraic expression equals a/b?
The algebraic expression is rational.
Why is the assumption that 2√3 - 1 is a rational number proven incorrect?
Because it leads to a contradiction that √3 is rational, which is false.
What is the correct conclusion when √5 + √3 is assumed to be a rational number?
The assumption is incorrect, and √5 + √3 is irrational.
Why is 2 - 3√5 proven to be an irrational number?
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What is the significance of a and b being co-prime positive integers in the proofs?
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How is the expression (a/b) - √3 rationalized in the proof that √5 + √3 is irrational?
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What is the common technique used in the proofs to establish the irrationality of algebraic expressions?
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Why does the expression (a² - 2b²)/2ab represent a rational number?
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What can be inferred about √2 + √3 based on the proof that √5 + √3 is irrational?
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What is the purpose of the proof by contradiction in these exercises?
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