Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
In which proof are both (p) and (q) found divisible by (5)?Which statement comes first in the proof sequence of (\sqrt{2})?Which statement comes near the end of the proof sequence of (\sqrt{3})?Which step is wrong in the proof of (\sqrt{5})?In the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5}), what type of numbers are (p) and (q) taken to be?If assuming (\sqrt{n}=\frac{p}{q}) and squaring gives (p^2=nq^2), which proof begins when (n=5)?Which fact is used correctly while proving the irrationality of (\sqrt{2})?Which property of (3) and (5) is useful in the proofs of (\sqrt{3}) and (\sqrt{5})?In an exam, what is the safest final sentence while writing the irrationality proof of (\sqrt{2}), (\sqrt{3}), or (\sqrt{5})?When assuming (\sqrt{2}) to be rational, what is the main reason for writing (p) and (q) as coprime?In the proof of irrationality of (\sqrt{2}), after assuming (\sqrt{2}=\frac{a}{b}), what is the next correct step?If (\sqrt{3}=\frac{a}{b}), where (a) and (b) are coprime, which condition about (b) is necessary?Why are (m) and (n) taken as coprime when (\sqrt{5}) is assumed rational and written as (\sqrt{5}=\frac{m}{n})?If (a^2=2b^2), by which number is (a^2) definitely divisible?If (a^2=3b^2), what conclusion about (a) is taken in the proof of (\sqrt{3})?If (a^2=5b^2), in which form can (a) be written?In the proof of (\sqrt{2}), if (a=2k), what is the correct value of (a^2)?In the proof of (\sqrt{3}), if (a=3k), what is the correct value of (a^2)?In the proof of (\sqrt{5}), if (a=5k), what is the correct value of (a^2)?Why is it a problem if both (a) and (b) are found even in the proof of (\sqrt{2})?