#### 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/ qwhere 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