Question

Prove that √8 is irrational

Answer 1

8 = 2 √2

Let 2 √ 2 be a rational number

=> 2 √ 2 = p/q. ( where p & q are integers but q not = 0)

=> √ 2 = p/(2q )

In the above statement is √2 which is an irrational number but RHS fraction, numerator is integer and denominator 2q is also an integer .
Also denominator is not equal to 0, since both 2 and q are not zero . This way all 3 conditions of rational number is fulfilled.
=> RHS is rational number
=> LHS not = RHS
Our assumption is wrong
Hence 2√2 is irrational
then √8 is also an irrational number