Question

Prove that square n is not a rational number, if n is not a perfect squar
State in each case, whether the given statement is True or False.​

Answer 1

If n is not a perfect square then  is irrational

Let on the contrary say it is rational .

Then

 where p and q are coprime integers.

so n =p2/q2

 

p2 =nq2

This shows p divides q

which is a contradiction.

Hence  is irrational if n is not a perfect square.