Prove that ` (3 + 5sqrt2)` is irrational.

Explanation

Let us assume, to the contrary , that ` (3 + 5sqrt2)` is rational.
Then , there exist co-primes a and b ` ( b ne0)` such that
` 3 +5sqrt2= a/b`
` Rightarrow 5sqrt2 = a/b -3 = (a -3b)/b`
` Rightarrow sqrt2 = (a-3b)/(5b)` is rational.
Thus, `sqrt2` is also rational.
But, this contradicts the fact that ` sqrt2` is irrational. So, our asumption is incorrect.
Hence, ` ( 3+5sqrt2)` is irrational.