Question

prove that 3+5√2 is irrational

Answer 1

take 3+5root2 be a rational number.

than

3+5root 2- 3= p/q.
5root×1/5=p/q
squaring both side
2=p square /q square
2q square =p square
so 2 divide p square
2 divide p also
let r be any positive integer

2qsquare = 4 r square
q square =2r square

2 divide q square
2 divide q also.

2 is only factor of p and q.

so 3 + 5 root 2 is not a rational number.

so 3+5 root 2 is an irrational no.