√2 = p/q
By squaring on both sides
2q2 = p2
p2 is an even number that divides q2
So p is an even number that divides q
Consider p = 2x where x is a whole number
Now substitute the value of p in 2q2 = p2,
2q2 = (2x)2
2q2 = 4x2
q2 = 2x2
q2 is an even number that divides x2.
So q is an even number that divides x
As both p and q are even numbers with a common multiple 2, which means that p and q are not coprime as the HCF is 2
It leads to a contradiction that root 2 is a rational number of the form p/q where p and q are coprime and q ≠ 0.
Therefore, root 2 is an irrational number using the contradiction method.
Prove that root 2 is an irrational number.
Root 2 is an irrational number.