Prove that root 2 is an irrational number.

√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.

Summary:

Prove that root 2 is an irrational number.

Root 2 is an irrational number.