Finding out if a number is rational or irrational.

Question

How does one find out if a given number is a rational number or irrational number?

Here is a related answer I posted: https://math.stackexchange.com/questions/62878/proving-irrationality/62885 — Michael Hardy, Jun 27 '17 at 05:57
. . . . . and another: https://math.stackexchange.com/questions/1683470/how-to-prove-log-23-is-irrational — Michael Hardy, Jun 27 '17 at 05:58
find out if a given number In what form or shape is the number "*given*" to you? — dxiv, Jun 27 '17 at 06:06
Generally contradiction is used to show this , like in p/q, q happens to be 0, or p&q resulting having a common factor but they must have not and much more things — Atul Mishra, Jun 27 '17 at 06:06

Atul Mishra · Answer 1 · 2017-06-27T06:34:20.437

In my high school , the first proof of irrationality I learned was of proof of irrationality of $\sqrt{2}$

The contradiction was used by me the first time and for last two years I am using this method to prove irrationality of numbers

If you want to know the proof of irrationality of $\sqrt {2}$ you can visit google or Wikipedia

Contradiction appears on some facts which are being obey by rational numbers but they must not obey that facts

Some of these can be derived from the definition of rational numbers such as

$1$. Rational number is of form $\frac{p}{q} , p,q$ belongs to intigers and $q\ne 0$

$2$. In $ \frac {p}{q}, p,q$ must be co prime , they cannot have common factors(this is standard notations of rational numbers)

If you are going with an irrational numbers starting with letting it rational and then in midway, you cross the properties of them, then you can say contradiction leads to the proof that the number is irrational

Some more things can be added to it...

Finding out if a number is rational or irrational.

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