Minimal polynomial

Number Theory Level 5

Let \( \alpha = \sqrt{5}-\sqrt{3}\), and let \( f(x) \) be the minimal polynomial of \( \alpha \). That is, \( f(x) \) is a monic polynomial with rational coefficients of the smallest possible nonzero degree such that \( f(\alpha) = 0 \).

Find \( f(1) \).