Question

prove that root 3+root 5 is irrational

Answer 1

let as assume root as rational 
so it has co-prime numbers  a&b
root 3 = a/b  
(squaring on both sides)
3=a square/ b square
* a square = 3b square (*)
: 3/a square & 3/a  - (1)

a =3c
(square on both sides)
a square = 9c square
apply (*)
3b square = 9c square
b square = 9c square / 3
               = 3c square
: b/3 square& b/3 -(2)
 in the view of (1) &(2)
 we can say our  assumption is wrong because both 1 & 2 has 3 as common factors. 
 therefore root 3 is irrational.


 now let as assume root5 as rational 
so it has co-prime numbers  a&b
root 5 = a/b  
(squaring on both sides)
5=a square/ b square
* a square = 5b square (*)
: 5/a square & 5/a  - (1)

a =5c
(square on both sides)
a square = 25c square
apply (*)
5b square = 25c square
b square = 25c square / 5
               = 5c square
: b/5 square& b/5      -(2)
 in the view of (1) &(2)
 we can say our  assumption is wrong because both 1 & 2 has 5 as common factors. 
 therefore root 5  is irrational.
 so the root 3 + root 5 is irrational 
 hence proved
 
 it helps u so plzz mrk as brainlist