x^2-5
=(x+√5)(x-√5)
x^8-16
=(x^4+4)(x^4-4)
=(x^4+4)(x^2+2)(x^2-2)
=(x^4+4)(x^2+2)(x+√2)(x-√2)
(3+√10)(√2-√5)
=3√2+2√5-3√5-5√2
=-√5-2√2