Question

Given that √2 irrational prove that (5+3√2) is in
rational number

Answer 1

let us assume that (5+3√2) is a rational number
then it can be represented in the form of p/q where q is not equal to 0.

i.e. 5+3√2 = p/q
3√2= p/q-5

3√2= p-5q/q
√2 = p-5q/3q


As p and q are integers therefore p-5q/3q is rational then √2 is also rational

which is not true therefore 5+3√2 is irrational

hope that help