Question

(3+5sqrt2)(4-sqrt2)

Answer 1

The approximate answer would be 26.04163056.......
Your minimal polynomial would be x^2-4x-574

Answer 2

just to clarify is this what you meant:
\[(3+5\sqrt{2})(4-\sqrt{2})\]

Answer 3

if you expand that out it becomes 12 - 3sqrt(2) + 20sqrt(2) - 5(2)
which is 2 + 17sqrt(2)

Answer 4

if so 3 times 4 is 12, 5 sqrt 2 times sqrt 2 is 5 sqrt 4 so that 4 would be out to 2 and 2 times 5 is 10 so 8-10 is -2 which is your answer.