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Show that √2 is irrational? |
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Answer» Let √2 is irrational number ,means √2 is a rational number .Let √2= p by q √2^2= p^2 by q^22 = p^2 by q^22q^2 = p^2 -------(1)q^2=p^2 by 2~2 divides p^2~2 divides p also. Let p by 2 =r ,for some integer r. p=2r ----------(2)On substituting eq.(2) in eq.(1). 2q^2=2^2.r^2q^2 = 4r^2q^2=2r^2q^2 by 2= r^2~2 divides q^2.~2 divides q also Thus, is a common factor of p and q but this contradict that p and q are coprime so our assumption is wrong .Hence ,√2 is an irrational number Let route to be a rational number so it can be written in p by Q form where p and q are coprime numbers means it has only one factor that is 1 and where is not equal to zero |
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