Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
Which option tells the role of assuming (\frac{p}{q}) in lowest form in the proof of (\sqrt{2})?If someone writes (p=5q) from (p^2=5q^2) in the proof of (\sqrt{5}), what type of error is it?In the proof of irrationality of (\sqrt{3}), which statement should come just before the final conclusion?Which statement deeply explains the role of squaring in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?In the proof of (\sqrt{5}), if (\frac{p}{q}) is in lowest form, which statement is correct when (p=5k) and (q=5r) are obtained?If both (p) and (q) are found even in the proof of (\sqrt{2}), which statement does it refute?Which option gives the correct further reasoning after substituting (p=3k) in the proof of (\sqrt{3})?Which statement proves that just because (5) is rational, (\sqrt{5}) does not become rational?Which option is the safest way to write the final conclusion in all three proofs?Which option best describes the correct common structure of the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?In the proof of (\sqrt{2}), after assuming (\sqrt{2}=\frac{a}{b}) in lowest form, (a^2=2b^2) is obtained. Which conclusion comes first according to proof order?Assume (\sqrt{3}) is rational and write (\sqrt{3}=\frac{p}{q}). What is the correct reasoning about (p) from (p^2=3q^2)?If (\sqrt{5}=\frac{m}{n}) is in lowest form and (m^2=5n^2), what is the next aim after writing (m=5k)?In the proof of (\sqrt{2}), after putting (a=2r), what correct form of (b^2) follows from (a^2=2b^2)?In the proof of (\sqrt{3}), after putting (p=3k), which middle equation is correct from (p^2=3q^2)?Which statement is algebraically wrong in the proof of (\sqrt{5})?If (a) and (b) are coprime, which result will immediately give a contradiction?In the proof of (\sqrt{2}), why is saying (b) is even immediately after proving (a) even an incomplete reasoning?In the proof of (\sqrt{3}), if (p=3r) and (q=3s), what is definite about (\gcd(p,q))?In the proof of (\sqrt{5}), which conclusion cannot be drawn immediately from (p^2=5q^2)?