Question

Prove that 3+5root2 is irrational.

Answer 1

let 3+5√2 be a rational number then
3+5√2=p/q
5√2=p/q-3
5√2=p-3q/q
√2=p-3q/q×1/5
√2=p-3q/5q
since √2=p-3q/5q=p/q.√2 is rational. but √2 is an irrational number. this is a contradiction to our assumption that 3+5√2 is rational. hence 3+5√2 is an irrational number

Answer 2

plz refer to this attachment