Podcast
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?
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?
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?
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?
Why is 2 - 3√5 proven to be an irrational number?
What is the significance of a and b being co-prime positive integers in the proofs?
What is the significance of a and b being co-prime positive integers in the proofs?
How is the expression (a/b) - √3 rationalized in the proof that √5 + √3 is irrational?
How is the expression (a/b) - √3 rationalized in the proof that √5 + √3 is irrational?
What is the common technique used in the proofs to establish the irrationality of algebraic expressions?
What is the common technique used in the proofs to establish the irrationality of algebraic expressions?
Why does the expression (a² - 2b²)/2ab represent a rational number?
Why does the expression (a² - 2b²)/2ab represent a rational number?
What can be inferred about √2 + √3 based on the proof that √5 + √3 is irrational?
What can be inferred about √2 + √3 based on the proof that √5 + √3 is irrational?
What is the purpose of the proof by contradiction in these exercises?
What is the purpose of the proof by contradiction in these exercises?
