Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
Which option is the correct final sentence to complete the proof of (\sqrt{3})?Which option shows that (p) and (q) are not coprime?In the proof of (\sqrt{5}), both (p) and (q) are found divisible by (5). This is against what?Which statement is correct for the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?In an exam, what should be clearly written in the last line of an irrationality proof?In the proof of (\sqrt{2}), if (q^2=2k^2) is obtained, what conclusion follows about (q)?In the proof of (\sqrt{3}), if (q^2=3k^2), what is the correct conclusion about (q)?In the proof of (\sqrt{5}), if (q^2=5k^2) is obtained, what is the next correct conclusion?Which option correctly shows the breaking of the coprime condition in the proof of (\sqrt{2})?Which option best describes the common idea in the proofs of (\sqrt{3}) and (\sqrt{5})?If (\sqrt{2}=\frac{p}{q}) is assumed in lowest form, what should be concluded first from (p^2=2q^2)?Assume (\sqrt{3}) is rational and (\sqrt{3}=\frac{a}{b}). If (a) and (b) are coprime, when will a contradiction occur in the proof?If assuming (\sqrt{5}=\frac{m}{n}) and squaring gives (m^2=5n^2), what is the correct next form for (m)?In the proof of (\sqrt{2}), if (p=2r), how does (p^2=2q^2) change?In the proof of (\sqrt{3}), after putting (a=3t), which form of (b^2) follows from (a^2=3b^2)?Which statement is a wrong step in the proof of irrationality of (\sqrt{2})?If (r) is prime and (r\mid x^2), which rule is used in irrationality proofs?In the proof of (\sqrt{5}), after putting (m=5k), which equation follows from (m^2=5n^2)?What is the role of assuming coprime numbers in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?If assuming (\sqrt{3}) rational gives (a^2=3b^2), what must be shown about (a) and (b) at the end?