Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
Which statement gives the final conclusion about (q) in the proof for (\sqrt{3})?Which type of proof is most commonly used to prove the irrationality of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?If both (p) and (q) are divisible by (3), what can be said about (\frac{p}{q})?Which option best expresses the main idea behind the irrationality of (\sqrt{2})?Why is (5\mid b) concluded from (5\mid b^2) in the proof for (\sqrt{5})?If (\sqrt{2}) were rational, why would its form (\frac{p}{q}) finally be rejected?Which statement is true in both proofs of (\sqrt{3}) and (\sqrt{5})?If (x^2) is even, what is the correct conclusion about (x)?Which option is a wrong conclusion in the proof for (\sqrt{5})?Which conclusion is correct for all three numbers (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?If (\sqrt{2}=\frac{p}{q}) is assumed in lowest form and (p^2=2q^2) is obtained, what is the most precise reason that (p) is even?When (\sqrt{3}) is assumed rational and written as (\sqrt{3}=\frac{a}{b}), why are (a) and (b) taken coprime?If (\sqrt{5}=\frac{x}{y}) and (x,y) are coprime, which conclusion follows immediately from (x^2=5y^2)?In the proof of irrationality of (\sqrt{2}), after putting (p=2r), which equation is correct?Which statement creates the actual contradiction in the proof for (\sqrt{3})?If (5\mid x^2), why is (5\mid x) concluded?In the proof for (\sqrt{2}), if both (p) and (q) are proved even, which final conclusion is appropriate?In the proof for (\sqrt{3}), after putting (a=3k), which correct conclusion follows?While proving (\sqrt{5}) irrational, after putting (x=5m), what is needed to conclude about (y)?Which option shows an incorrect argument in the proof of irrationality of (\sqrt{2})?