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