Mathematics
Proof of irrationality of √2, √3, √5
Practice questions
In the proof of (\sqrt{3}), if both (a) and (b) are found divisible by (3), which condition is broken?In the proof of (\sqrt{5}), what does finding both (a) and (b) divisible by (5) show?Which statement shows the correct order for the proof of (\sqrt{2})?In the proof of (\sqrt{3}), which wrong conclusion should not be taken directly from (a^2=3b^2)?In the proof of (\sqrt{5}), what is the correct first conclusion from (a^2=5b^2)?Which statement correctly explains the method of contradiction?In the proof of (\sqrt{2}), when (a) is even, we write (a=2k). What type of number is (k)?What is the basis for writing (a=3k) in the proof of (\sqrt{3})?In the proof of (\sqrt{5}), after writing (a=5k), what is the next aim?Which option states the contradiction in the proof of (\sqrt{2}) correctly?Why can (\sqrt{2}), (\sqrt{3}), and (\sqrt{5}) not be directly treated as integers?Which square root is not an example of irrationality proof in this chapter because it is rational?If (\sqrt{2}) were rational, in what type of form could it be written?If (\sqrt{5}=\frac{a}{b}), what will the left side become after squaring?If \(\sqrt{3}=\frac{a}{b}\), what will the right side become after squaring?Which option gives the correct result of taking (\frac{a}{b}) in lowest form in the proof of (\sqrt{2})?If assuming (\sqrt{3}) rational makes both (a) and (b) divisible by (3), what is the correct conclusion?Which statement completes the proof of irrationality of (\sqrt{5})?Which rule is repeatedly used in the proof of (\sqrt{2})?Which rule is equally useful in the proofs of (\sqrt{3}) and (\sqrt{5})?