Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
In the proof of (\sqrt{2}), after putting (a=2k), what follows from (4k^2=2b^2)?In the proof of (\sqrt{3}), what correct conclusion follows from (9k^2=3b^2)?In the proof of (\sqrt{5}), what correct conclusion follows from (25k^2=5b^2)?In which situation can (\frac{a}{b}) not be called lowest form?In the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5}), what becomes impossible at the end?Which option is the correct beginning of the proof of irrationality of (\sqrt{3})?Which option is a correct middle step in the proof of (\sqrt{5})?In the proof of (\sqrt{2}), if both (a) and (b) are even, what is at least one common factor of them?In the proof of (\sqrt{3}), if (a=3k) and (b=3l), what can be said about (a) and (b)?Why are results like (a=5k) and (b=5l) a contradiction in the proof of (\sqrt{5})?In which proof is the prime factor (2) used mainly?In which proof is the prime factor (3) used mainly?In which proof is the prime factor (5) used mainly?Which option is a wrong reason in the proof of (\sqrt{2})?Which option is a wrong statement in the proof of (\sqrt{3})?Which option is a wrong statement in the proof of (\sqrt{5})?Which option explains why (\sqrt{2}) cannot be rational?Which option is the correct short reason for the irrationality of (\sqrt{3})?Which option is the correct short reason for the irrationality of (\sqrt{5})?In an exam, what should be clear in the final line while proving (\sqrt{2}), (\sqrt{3}), or (\sqrt{5})?