prove root3 is irrational
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•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!!!
•√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!!!
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