Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
If someone writes (b) is even directly from (a^2=2b^2) in the proof of (\sqrt{2}), what is the mistake?In the proof of (\sqrt{5}), both (p) and (q) are found divisible by (5). What does this reveal?Which option correctly completes the proof of irrationality of (\sqrt{3})?If assuming (\sqrt{2}) rational makes (\frac{a}{b}) not remain in lowest form, what is the conclusion?Which option correctly identifies the proof of (\sqrt{3})?In the proof of (\sqrt{2}), if (a=2k) is obtained from (a^2=2b^2), what is true about (k)?Which option gives a true statement with a wrong reason in the proof of (\sqrt{5})?What is the purpose of substituting (p=3k) in the proof of (\sqrt{3})?Which statement is the biggest common misconception in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Which option shows the correct route to prove (q) divisible by (5) in the proof of (\sqrt{5})?In the proof of (\sqrt{2}), if (a=2m) and (b=2n), what does this go against?In the proof of (\sqrt{3}), which statement is correct but not the final conclusion?Which option is the correct correction of the wrong argument that (\sqrt{5}) is rational?In the proof of (\sqrt{2}), what type of error is directly writing (a=2b) from (a^2=2b^2)?In the proof of (\sqrt{5}), which statement should come just before the final contradiction?While writing the final line in all three proofs, which sentence is the safest?Which option gives the correct common structure of the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?In the proof of (\sqrt{2}), (a) has been proved even and (\frac{a}{b}) is in lowest form. What is the most correct next step?How can (p^2=3q^2) in the proof of (\sqrt{3}) be understood using exponents of prime factors?In the proof of (\sqrt{5}), if finally (p=5m) and (q=5n) are obtained, what is the most accurate comment on the lowest form of (\frac{p}{q})?