Question

prove root3 is irrational

Answer 1

•Let us assume that √3 is rational.

•√3=p/q (where p and q are coprimes and q is not equal to zero)

•Squaring on both sides

•We get,

•3=p^2/q^2

•p^2=3q^2......(i)

•Here 3divides p^2

•Therefore 3divides p

•Hence 3 is a factor of p.

•p/3=c

•Squaring on both sides

•p^2/9=c^2

•p^2=9c^2......(ii)

•From (i) and (ii)

•3q^2=9c^2

•q^2=3c^2

•Here 3 divides q^2

•Therefore, 3 divides q

•Hence 3 is a factor of q.

•Here 3 is a factor of both p and q.

•But p and q are coprimes.

•So, this contradicts to our assumption.

•Therefore, we can say that √3 is irrational number.

Hope it helps u!!!

Answer 2

Hope it helps.......

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