Polynomials with Integer Coefficients and irrational roots Is there a polynomial with integer coefficients which has √2 +√7 ￼ as a root?

$$
x = \sqrt{2} + \sqrt{7} \\ (x-\sqrt{2})^2=7 \\ x^2-2\sqrt{2}x+2=7 \\ x^2-5=2\sqrt{2}x \\ (x^2-5)^2=8x^2 \\ x^4-18x^2+25=0
$$
