Question

Prove that √3 is an irrational number

Answer 1

and that's the ans take 3 in place of 5

Answer 2

proof:- IF Possible,
let √3 be rational and let it's simplest form be a/b .
then , a and b are intergers having no common factor other than 1, and b≠0.
now, √3= a/b = 3=a²/b² (on squaring both sides)
3b²=a² ..........(1)
3 divides a² (therefore 3 divides 3b²)
3 divides a
(therefore 3 is a prime and 3 divides a) .
let a=3c for some integers c.
putting a=3c in(1) we get:
3b²= 9c²= b²=3c²
3 divides b²(therefore 3 divides 3c²)
3 divides b
(3 Is prime and 3 divides b² = 3 divides b).
thus, 3 is a common factor of a and b.
but this is contradicts the facts that a and b have no common factor other than 1.
the contradiction arises by assuming that √3 Is irrational.
hence, √3 Is irrational.
............................MENTAL
hope,