### Video Transcript

Is the square root of two a
rational or an irrational number?

Letβs begin by recalling what a
rational number is. A rational number is a number that
can be expressed as a fraction π over π where π and π are integers and π is not
equal to zero. And an irrational number is a
number that is not rational. So, here we have the square root of
two. We know that the square root of two
lies between the square root of one and the square root of four since one and four
are the nearest square numbers. The positive value of the square
root of one is one, and the positive value of the square root of four is two.

Using a calculator, we can evaluate
the square root of two as a 1.414213562 and continuing. The decimal is not a repeating
decimal. And we can also see that this
decimal does not terminate. Therefore, we could not write a
fraction to represent this decimal that represents the square root of two, meaning
that the rational definition would not fit, which means that the square root of two
is an irrational number.