Question

prove that√3 is an irrational number

Answer 1

Under root 3 is an irrational number since it cant be expressed in the form of p/q

Answer 2

Let assume √3 be a rational number

Where

√3=a/b______(where a and b are co prime number and there HCF is 1)

√3b=a

Square both side

3b²=a²

a² is a factor of 3

a is also a factor of 3__________(by theorm)

Let a=3c___________________(some integer)

Square both side

a²=9c²

3b²=9c²__________________(by theorm)

b²=3c²

b² is a factor of 3

b is also a factor of 3________(by theorm)

Here both a and b are factor of 3 and are not co prime number

Which contradict our assumption wrong

So √3 is irrational number