Question

Prove that root 2,3,5 is an irrational no

Answer 1

let root2 be rational number
root2=p/q
root 2 has an factor other than 1
now we cancel out that factor.
root2=a/b eq.1
 root 2b=a
squaring on both side
2bsquare=a square
here 2 is divisible by a square then by theorem of fundamental arithmetic 2 is also divisible by a
now root2 do not have any factor other than 1
A=2C 2 eq.
put the value of eq. 1 in eq 2
root 2b =2C
squaring on both side 
2b square=4 Csquare
hre 2 is also divisible by b then by theorem 1.3 2 is also divisible by b
so our assumption become wrong 
since we prove that a and b do not have any common factor other than 1 but here 2 is a common factor
therefore root 2 is an irrational number.

for other the process is same only you have to change the digit