Question :

Prove that √ 3 is an irrational number
Submitted on 3/3/2024 | Answered by Vandana Rana

Answer :

lets us assume this is rational number
then
√
3
=
p/
q



where p and q are co primes.

or
q
√
3
=
p


squaring both sides

3
q²

=
p²




So 3 divides p²,from theorem we know that,
3 will divide p also.
p=3c


3
q²

=
9
c²



or
q²

=
3
C²



So q divided by 3 also


So both p and q are divided by 3
p and q are not co-prime.
which is contradiction from we assumed

So
√
3
is irrational number