Question

Prove the following are irrational
(1) 1/√2
(2) √3+√5

Answer 1

1) 1/√2=p/q (assume that it is a rational )

 √2=Q/p  ... So it is irrational......








2) √3+√5=p/q (assume that it is a rational )

squaring on both sides 

(√3+√5)*2=(p/q)*2

3+5+2√3*√5=p*2/q*2

2√15=p*2/q*2-8

√15=p2-8q2/2q*2  hence it is irrational

Answer 2

They both are irrational because all non-square Numbers are considered as irrational numbers