Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
In the proof of (\sqrt{5}), after (p^2=5q^2), when is (q) proved divisible by (5)?If (a^2=2b^2) and (a=2k), what is true about (b^2)?Which option is common in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?A student writes (\sqrt{3}=\frac{p}{q}), so (3=\frac{p}{q}). What is the mistake?In the proof of (\sqrt{5}), what does taking (\frac{p}{q}) in lowest form mean?Which statement correctly tells the role of factor (2) in the proof of (\sqrt{2})?In the proof of (\sqrt{3}), if (p=3k), what is the correct value of (p^2)?Which option gives the correct final reason in the proof of (\sqrt{5})?If (p) and (q) are coprime, which situation is impossible?After assuming (\sqrt{2}) rational, (\sqrt{2}=\frac{p}{q}) is written. If finally both (p) and (q) are even, what is the correct conclusion?Which option correctly states the effect of both (p) and (q) being divisible by (3) in the proof of (\sqrt{3})?Which statement is a correct middle step in the proof of irrationality of (\sqrt{5})?If (q^2=3k^2) is obtained in the proof of (\sqrt{3}), what is the correct conclusion for (q)?In the proof of (\sqrt{2}), which statement is correct but an incomplete conclusion?In the proof of (\sqrt{5}), why is getting (q^2=5k^2) after putting (p=5k) important?Which option shows a wrong idea in all three proofs?In the proof of (\sqrt{2}), if both (p) and (q) are even, which statement about (\frac{p}{q}) is correct?If the rational assumption for (\sqrt{3}) is proved false, what is the correct final conclusion?Which statement corrects the wrong argument that (\sqrt{5}) is rational?Which option is the correct final sentence of the proof of (\sqrt{2})?