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2014-07-22T18:41:01+05:30
The answer is : 
1. for √2
let us assume√2 as a rational no
so √2=p/q
squaring on both sides 
√2²=p²/q²
2=p²/q²
p²=2q² 
so 2 divides p²
⇒ 2 divides p
let p= 2m
squaring on both sides
p²=4m²
⇒2q²=4m²
q²=2m²
so 2 divides q² ⇒ 2 divides q 
this contradicts the fact that p & q are co primes and have only one common factor so our assumption is wrong therefore √2 is irrational 

for √3 
the same method but take p=3m and then you can prove it 
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