Question 10
Prove that 3+5 irrational
Let us suppose that 3+5 is rational.
Let 3+5=a is rational.
Therefore, 3=a5             
On squaring both sides, we get,
(3)2=(a5)2
 3=a2+52a5
[ (ab)2=a2+b22ab]
 2a5=a2+2
Therefore,  5=a2+22a    
As the right hand side is rational number while 5 is irrational. It contradicts with our assumption.
Hence, 3+5 is irrational.