Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
What is the correct order of the proof of (\sqrt{2})?If (\sqrt{3}) were rational, how would it be written in lowest form?Which option shows an incomplete proof of (\sqrt{5})?What is the importance of getting (q^2=2k^2) in the proof of (\sqrt{2})?In the proof of (\sqrt{3}), why is (q) not directly said to be divisible by (3) from (p^2=3q^2)?Which statement is the common final idea in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?In the proof of (\sqrt{5}), which rule is used to go from (p^2=5q^2) to (p=5k)?In the proof of (\sqrt{2}), if (p=2k) and (q=2r) are obtained, what can be said about (\frac{p}{q})?In the proof of (\sqrt{3}), if (p=3k) and (q=3r) are obtained, what is the correct conclusion?Which option shows the correct order in the proof of (\sqrt{5})?In which proof does finding both (p) and (q) even give the final contradiction?In a proof, (p^2=3q^2), (p=3k), and (q^2=3k^2) appear. This proof is related to which square root?Which statement justifies that (a) is even when (a^2) is even in the proof of (\sqrt{2})?Which statement is a wrong reasoning in the proof of (\sqrt{5})?Which option tells the main purpose of squaring in all three proofs?In the proof of (\sqrt{3}), after getting (q^2=3k^2), which form can be written for (q)?In the proof of (\sqrt{2}), both (p) and (q) being even makes which statement false?If assuming (\sqrt{5}) rational leads to a contradiction, what is the conclusion according to the contradiction method?Which option gives the correct difference between the proofs of (\sqrt{2}) and (\sqrt{5})?Which option shows the common logic in the proofs of (\sqrt{3}) and (\sqrt{5})?