Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
In the proof of (\sqrt{5}), after getting (n^2=5k^2), which reasoning is correct?Which option gives the correct short structure of the proof of (\sqrt{2})?If (\sqrt{2}) were rational, what conclusion follows if both (p) and (q) are found even in lowest form (\frac{p}{q})?Which statement is correct in the proof of (\sqrt{3}) but is not the main step in the proof of (\sqrt{2})?Which option correctly tells the role of (5) being prime in the proof of (\sqrt{5})?After assuming (\sqrt{3}) rational, (\sqrt{3}=\frac{p}{q}) is written. If common factor (3) is found in (p) and (q), which assumption is proved false?If (p) and (q) are coprime, which of the following situations is impossible?In proving (\sqrt{2}), if (q) is also proved even, what conclusion follows about (p) and (q)?Which statement gives the correct order of the proof of (\sqrt{5})?If (\sqrt{2}=\frac{p}{q}) and (p), (q) are coprime, proving both (p) and (q) even contradicts what?Which option gives the correct reason for writing (a=3k) in the proof of (\sqrt{3})?Which option is the common final idea in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Which statement is correct in the proof of (\sqrt{5})?In the proof of (\sqrt{3}), what does getting (p=3r) and (q=3s) show?If assuming (\sqrt{2}) rational finally gives (q=2s), why is this important in the proof?Which statement is directly correct from (p^2=5q^2)?Which option gives the correct meaning of the coprime condition for (p) and (q) in the proof of (\sqrt{2})?In the proof of (\sqrt{3}), which step is done to remove the square root?If in the proof of (\sqrt{5}), both (p) and (q) are proved divisible by (5), what does it mean?Which option correctly shows a difference between the proofs of (\sqrt{2}) and (\sqrt{5})?