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Irrational Numbers


Consider the value of $\pi$. The Value of $\pi$ = 3.145926535897932384626433882795.... and so on. Here we could observe that the Decimal Place value of $\pi$ is not repeating. Similarly many kind of numbers are there in maths which are not repeating. These are called irrational numbers.

The decimal Real Numbers which are not Rational Numbers are called Irrational numbers as these numbers are not expressed in the fractional form.

Irrational Number Definition

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Irrational numbers is defined as the number which cannot be expressed in the form $\frac{p}{q}$, where p and q are integers and q $neq$ 0.


  1. The best example is value of $\pi$ is solved to over one million decimal places and still there is no pattern found.
  2. Square root of every non perfect Square is an irrational number and similarly, a Cube root of non-perfect cube is also an example of the irrational number.

When we multiply any two irrational Numbers and the result is rational number, then each of these irrational numbers is called rationalizing factor of the other one.