Question

prove that root 2 is irrational

Answer 1

Let √2 be a rational number 

Therefore, √2= p/q 

On squaring both sides, we get 

                  p²= 2q²                  ----- 1                                                                 

Clearly, 2 is a factor of 2q²

= 2 is a factor of p²                                                                    

= 2 is a factor of p

 Let p =2 m for all m

Squaring both sides, we get 

           p²= 4 m²                     ----- 2                                                                    

From 1  and 2 we get 

          2q² = 4m²      =      q²= 2m²

Clearly, 2 is a factor of 2m²

= 2 is a factor of q²                                                    

= 2 is a factor of q 

Thus, we see that both p and q have common factor 2 which is a contradiction that H.C.F. of ( p,q ) = 1

Therefore, Our supposition is wrong

Hence √2 is not a rational number i.e., irrational number.

Answer 2

Hey your answer.

Hope it helps....

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