Video: Determining If a Number Is Rational or Irrational

Is √2 a rational or an irrational number?

01:11

Video Transcript

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

Let’s begin by recalling what a rational number is. A rational number is a number that can be expressed as a fraction 𝑝 over π‘ž where 𝑝 and π‘ž are integers and π‘ž 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.

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