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Prove that root 3 is an irrational |
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Answer» IET root3 be rational and let its simplest form be a/b then aAnd b are integers having no common factor other than 1 and( b not equal to 0) now,√3= a/b=3=asquare/bsquare,•=3bsquare=asquare,3dividea[3 is prime and 3divides a square=3,divides a] let a=3c(putting a=3c in(1) we get 3b square=9c square=b square=3c square,=3divides b square [3divides 3c square]=3 divides b[3 is prime and 3 divides b square = 3divides b],3 is a common factor of a AND b see ncert text book for d same |
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