Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
If (\sqrt{2}) is rational and (\sqrt{2}=\frac{p}{q}), which equation is obtained after squaring?In the proof of irrationality of (\sqrt{5}), why does (a^2=5b^2) imply that (a) is divisible by (5)?In which situation can (\frac{p}{q}) not be called lowest form?If (p^2=3q^2) in the proof for (\sqrt{3}), in what form should (p) be correctly written?Which statement is correct for (\sqrt{2}) but not directly correct for the usual proof of (\sqrt{3})?In the proof for (\sqrt{5}), if both (a) and (b) turn out divisible by (5), what conclusion is correct?Which option gives the correct contradictory result after assuming (\sqrt{2}) rational?If someone writes (p^2=3q^2), therefore (p=3q), why is this wrong?What is the first assumption made while proving the irrationality of (\sqrt{5})?Which statement is correct if (n) is an odd integer?If (p) and (q) are coprime, which of the following is impossible?Which option gives a proper final sentence for proving the irrationality of (\sqrt{3})?If (p^2=5q^2) and (5\mid p), after putting (p=5k), what will (q^2) equal?Which property in the proof of (\sqrt{2}) is directly connected with (2) being prime?Which option correctly explains proof by contradiction in irrationality proofs?If (p,q) are coprime in (\sqrt{2}=\frac{p}{q}), what does it indicate when both (p) and (q) turn out even?In the proof for (\sqrt{3}), if (p=3k), what is (p^2) equal to?Which option clearly shows that assuming (\sqrt{5}) rational is wrong?Which option is a correct example of an irrational square root because it is not a perfect square?If a student does not write (q\neq0) while proving (\sqrt{2}) irrational, what is missing?