Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
What opposite assumption is taken while proving the irrationality of (\sqrt{2})?Which condition is necessary while writing (\sqrt{3}=\frac{p}{q})?If (\sqrt{5}=\frac{p}{q}), which equation is obtained after squaring both sides?If (p^2) is divisible by (2), what is the correct conclusion about (p)?If (p^2=3q^2), by what is (p^2) divisible?In the proof of (\sqrt{5}), what is the first correct conclusion from (p^2=5q^2)?If (p) is divisible by (3), what is the correct form of (p)?In the proof of (\sqrt{2}), if (p=2k), what is the correct form of (p^2)?In the proof of (\sqrt{5}), if (p=5k), what will (p^2) be?In the proof of (\sqrt{3}), after putting (p=3k), we get (9k^2=3q^2). What follows from this?If both (p) and (q) are found even, why can they not be coprime?What creates the contradiction in the proof of (\sqrt{5})?Which prime factor plays the main role in proving (\sqrt{3}) irrational?Which method is common in proving the irrationality of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?If a fraction is in lowest form, what is true about its numerator and denominator?In the proof of (\sqrt{2}), which wrong conclusion should not be drawn directly from (p^2=2q^2)?Which statement is not correct in the proof of (\sqrt{5})?What is the correct beginning of the proof of irrationality of (\sqrt{3})?If (p^2) is divisible by (5), what conclusion is taken about (p)?In the proof of (\sqrt{2}), what follows from (4k^2=2q^2)?