Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
Which difference is correct when comparing the proofs of (\sqrt{3}) and (\sqrt{5})?Which statement would weaken the proof of (\sqrt{2}) the most?If (3\mid p), in which form is it proper to write (p)?In the proof of (\sqrt{5}), after proving from (p^2=5q^2) that (p) is divisible by (5), what is the next correct step?Which statement shows that (\sqrt{2}) cannot be an integer?In the proof of irrationality of (\sqrt{3}), if both (p) and (q) are divisible by (3), what will be said about the fraction?If (2\mid q^2), what conclusion about (q) is taken in the proof for (\sqrt{2})?Why is it impossible for both (p) and (q) to be divisible by (5) in the irrationality proof of (\sqrt{5})?Which option gives the correct final sentence for proving the irrationality of (\sqrt{2})?In the proof for (\sqrt{3}), if (p=3r), what is the correct value of (p^2)?Assuming (\sqrt{5}) rational gives (p^2=5q^2). If (p=5r), which simplification is correct?Which statement correctly relates perfect squares and irrational square roots?If (p) and (q) are coprime, why can (p=5m) and (q=5n) not hold together?Which part of the proof of irrationality of (\sqrt{2}) shows proof by contradiction?In the proof for (\sqrt{3}), after (p^2=3q^2) shows (p) divisible by (3), what is the correct path to reach (q)?Which option is unnecessary in the proof of irrationality of (\sqrt{5})?In the proof for (\sqrt{2}), after getting (q^2=2r^2), why is (q) even?If (\sqrt{3}) were rational, what inconsistency would finally appear in the proof?Which statement is not correct in the proof for (\sqrt{5})?What main exam lesson is learned from the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?