Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
In a proof, (p^2=5q^2), then (p=5k), then (q^2=5k^2) are obtained. This is related to the irrationality of which number?Which option is the correct chain to reach (q) in the proof of (\sqrt{3})?Which option correctly states the main contradiction used in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?In the proof of (\sqrt{2}), if (p) and (q) are coprime, why is getting (p=2k) and (q=2r) impossible?Which statement is correct in proving (\sqrt{5}) irrational?A student writes (q=2k) from (q^2=2k^2) in the proof of (\sqrt{2}). What is the correct comment?Which option explains why the rational assumption for (\sqrt{3}) breaks?What is the main purpose of squaring in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?If assuming (\sqrt{5}) rational leads to a contradiction, what is proved true?In an exam, which precaution is most important while writing the irrationality proof of (\sqrt{2}), (\sqrt{3}), or (\sqrt{5})?Assume (\sqrt{2}) is rational and written as (\sqrt{2}=\frac{a}{b}). If (\frac{a}{b}) is in lowest form, what is true about (a) and (b)?In the proof of (\sqrt{3}), after assuming (\sqrt{3}=\frac{p}{q}), which correct equation is obtained by squaring?If (\sqrt{5}=\frac{m}{n}) and (m^2=5n^2), what is the first correct conclusion about (m^2)?In the proof of irrationality of (\sqrt{2}), after getting (a^2=2b^2), which is the correct form for (a)?In the proof of (\sqrt{3}), after putting (p=3k), how does (p^2=3q^2) change?In the proof of (\sqrt{5}), after putting (p=5k), what form of (q^2) follows from (p^2=5q^2)?Which option is not correct in the proof of (\sqrt{2})?If (r) is prime and divides the square (x^2) of an integer (x), what is the correct conclusion?In the proof of (\sqrt{3}), if both (p) and (q) are found divisible by (3), what does this contradict?In the proof of (\sqrt{5}), after getting (q^2=5k^2), which reasoning is correct?