Prove that (5 + 3) is irrational.

Given: (5 + 3)

To prove: It is irrational.

Explanation:

Assume that 5 + 3√2 is rational
,

where a and b are integers.


we know that a, b, 3 and 5 are integers and they are also rational {i.e RHS is rational}
therefore √2 will be rational.
but we know that √2 is irrational.
there is a contradiction
so, 5 + 3√2 is an irrational number.