H1, Why pi (π) is a irrational number

Why pi (π) is a irrational number (अपरिमय  संख्या )?

π is defined as the ratio of circumference (c) of the circle to its diameter (d)

  i.e. π = c/d this seems to contradict the fact that π is an irrational.

We can resolve this contradiction in this way.

When we measure the length with a scale or with any other device, we can get an approximate rational value, i.e.  c and d both are irrational.

So c and d are irrational and hence π is irrational ( ratio of two different irrational number is always irrational.)

The Greek genius Archimedes was the first to compute digits in the decimal expansion of π .  He find out 3.140845 < π < 3.142857.

Why root 2 is irrational

there are two types of decimals 

1 Terminating decimals              2 Non terminating decimals 

Again non terminating decimals have two category 

1 Recurring or repeating decimals   2 Non recurring or non repeating decimals 

All non terminating non recurring decimals are IRRATIONAL NUMBERS 

Since root 2 is non terminating non recurring decimal therefore it is a irrational number