Question

prove that root 3 + root5 is irrational​

Answer 1

root 5+3
or root 5+9
or root 14
or 3.74165... is not terminating and non repeating so it is irrational no.
 pls mark it brainliest answer i need 1 brainliest answer for my rank

Answer 2

let us think that root 3+root 5 is rational.
root3+root5=a/b  (where a,b are integers and b is not equal to 0 )
root3= a/b-root5
squaring on both sides,
3=a2/b2-2*a/b*root5+5
2a/broot5 =a2/b2-2
root5=a2-2b2   *  b/2a
               b2

 root5=a2-2b2
                2ab
if a2-2b2  is rational then root 5 is also rational.
     2ab
       
but this contradicts the fact that root 5 is irrational.
this has been arisen due to our wrong assumption that root3+root5 is rational
so, root3+root5 is irrational.