Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
Which option shows a similarity between the proofs of (\sqrt{3}) and (\sqrt{5})?A student writes in the proof of (\sqrt{2}) that (p^2) is even so (p) is even. Why is this step correct?If assuming (\sqrt{5}) rational finally gives a contradiction, which conclusion is correct?Which statement correctly tells the final conclusion about (b) in the proof of (\sqrt{3})?In the proof of (\sqrt{2}), if both (p) and (q) are even, what can be said about the fraction (\frac{p}{q})?Which statement correctly explains why (q\neq 0) is needed in the proof of (\sqrt{2})?In a proof, (p^2=3q^2) is obtained. This is related to the irrationality proof of which square root?In a proof, from (p^2=2q^2), we get (p=2r) and then (q=2s). What contradiction does this give?In the proof of (\sqrt{5}), (p) is found divisible by (5) from (p^2=5q^2). What is the purpose of putting (p=5k)?Which statement leaves the proof of (\sqrt{3}) incomplete?Which option is the correct use of the definition of rational number in the proof of (\sqrt{2})?If (\sqrt{3}) is assumed rational and written as (\frac{p}{q}), what is the benefit of taking (\frac{p}{q}) in lowest form?Which option shows the correct path to prove (q) divisible by (5) in the proof of (\sqrt{5})?Which statement is a wrong simplification after putting (p=2k) in the proof of (\sqrt{2})?In the proof of (\sqrt{3}), from (p^2=3q^2), (p) is divisible by (3). This is based on which rule?In which situation is the rational assumption for (\sqrt{2}) proved false?A student wrote that (\sqrt{5}) is rational because (5) is rational. What is the mistake in this reasoning?Which option gives both the correct final conclusion and reason in the proof of (\sqrt{3})?Which option is a wrong method in all three proofs?In an exam, what is the most important final line while proving the irrationality of (\sqrt{2}), (\sqrt{3}), or (\sqrt{5})?