Proof by contradiction : show that √ 2 is irrational.

is irrational

Step-by-step explanation:

Let us assume that is rational. Thus, it can be expressed in the form of fraction , where x and y are co-prime to each other.

=

Squaring both sides,

Now, it is clear that x is an even number. So, let us substitute x = 2u

Thus,

Thus, is even, which follows the fact that y is also an even number. But this is a contradiction as x and y have a common factor that is 2 but we assumed that the fraction  was in lowest form.

Hence, is not a rational number. But is a an irrational number.

answer: check all that apply, where the options?

step-by-step explanation: