(squareroot 3+squareroot 5)^2=8+2 squareroot 15
(sqrt(3) + sqrt(5) )^2 = (sqrt(3) + sqrt(5) ) * (sqrt(3) + sqrt(5) )
Multiplying out this gives
3 +sqrt(3)sqrt(5)+ sqrt(3)sqrt(5) + 5
= 8 + 2 (sqrt(3)sqrt(5))
using the rule sqrt(a) * sqrt(b) = sqrt(a*b)
= 8+2 sqrt(15)