why root 5 upon 2 is not a rational no.

If  ( √5 / 2 ) is a rational number , then we write ( √5 / 2 ) as

 

( √5 / 2 ) = p / q 

 

where p and q are integer

 

Then , we rewrite above expression as 

 

√5  = ( 2p) / q 

 

where 2p is another integer .

 

It means √5 is expressed as fraction so that an integer divided by other integer which is not true

 

because we know that √5 is irrartional number .

 

Hence our initial assumption ( √5 / 2 ) = p / q  is false .

 

Hence ( √5 / 2 ) is not a rational number