Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
In the proof of (\sqrt{5}), what correct conclusion follows from (25k^2=5q^2)?Which square root is rational, so an irrationality proof like (\sqrt{2}) does not apply to it?Why are (\sqrt{2}), (\sqrt{3}), and (\sqrt{5}) not taken as integers?If (\sqrt{2}) is rational, in which form can it be written?If \(\sqrt{3}=\frac{p}{q}\), what does the right side become after squaring?When (\sqrt{5}=\frac{p}{q}) is squared, what does the left side become?Which statement correctly states the prime factor rule?What is proved at the end in the proof of (\sqrt{2})?Which option correctly states the final contradiction in the proof of (\sqrt{3})?In the proof of (\sqrt{5}), after writing (p=5k), what is the next aim?What is the main reason for writing (p) and (q) coprime in the proof of (\sqrt{2})?If both (p) and (q) are divisible by (5), what happens to their being coprime?Which option is the correct short reason for the irrationality of (\sqrt{2})?Which statement is a wrong step in the proof of (\sqrt{3})?In the proof of (\sqrt{2}), after (p) is found even, what type of number is (k) in (p=2k)?Which option gives the correct order of the proof of (\sqrt{2})?In the proof of (\sqrt{5}), after (p^2=5q^2), what is the correct form for (p)?If the rational assumption leads to a contradiction, what is the conclusion about the original statement?In which proof are both (p) and (q) found divisible by (2)?Which statement is correct for the proof of (\sqrt{2})?