Using any method of validating Mathematical statements, prove that √3 is irrational - Maths - Mathematical Reasoning

Question

Using any method of validating Mathematical statements, prove that
√3 is irrational

Neha Sethi · Accepted Answer

Dear student
Let p be the statement given by p: 3 is irrational 
If possible,  let p be not true  i
e let p be false Thenp is false 
⇒3 is rational 
⇒3=ab , where a  and b are integers having no common factor
⇒3=a2b2⇒3b2=a2⇒a2=3b2⇒3 divides a2⇒3 divides a⇒a=3c for some integer c⇒a2=9c2⇒3b2=9c2    as 3b2=a2⇒b2=3c2⇒3 divides b2⇒3 divides bThus, 3 is common factor of both a and b 
This contadicts that  a  and b have no common factorSo, the supposition was wrong 
Hence '3 is irrational'  is true
Regards

Using any method of validating Mathematical statements, prove that √3 is irrational.