Question 1004699
the problem is:


(5 + sqrt(6)) * (5-sqrt(2))


you would multiply these using the distributive law of multiplication, same as you would any other multiplication of this  type.


distributive law of multiplication says:


(a + b) * (c + d) = ac + ad + bc + bd


in this problem that becomes:


(5 + sqrt(6)) * (5-sqrt(2)) = 5 * 5 - 5 * sqrt(2) + sqrt(6) * 5 - sqrt(6)*sqrt(2)


you would then simplify:


5*5 = 25
5 * sqrt(2) = 5 * sqrt(2)
sqrt(6) * 5 = 5 * sqrt(6)
sqrt(6)*sqrt(2) = sqrt(6*2) = sqrt(12) = sqrt(4*3) = 2*sqrt(3)


put them all together and you get:


(5 + sqrt(6)) * (5-sqrt(2)) = 5 * 5 - 5 * sqrt(2) + sqrt(6) * 5 - sqrt(6)*sqrt(2) becomes:


(5 + sqrt(6)) * (5-sqrt(2)) = 25 - 5 * sqrt(2) + 5 * sqrt(6) - 2 * sqrt(3)


there are no common terms that can be combined any further.


i believe this is as simple as it can get.