Posted by Jon on .
Assume that no denominator equals 0.
sqrt12  sqrt18 + 3sqrt50 + sqrt75
= (sqrt2^2*3)  (sqrt2*3^2) + (3sqrt2*5^2) + (sqrt3*5^2)
= (sqrt2^2*sqrt3)  (sqrt3^2*sqrt2) + (3sqrt5^2*sqrt2) + (sqrt5^2*sqrt3)
= (2*sqrt3)  (3*sqrt2) + (3sqrt5*sqrt2) + (5*sqrt3)
= 7sqrt3 + sqrt2 + sqrt5(answer)

Algebra II (check) 
Reiny,
no, your roots 3's are ok, but....
sqrt12  sqrt18 + 3sqrt50 + sqrt75
= √(4*3)  √(9*2) +3√(25*2) + √(25*3)
= 2√3  3√2 + 15√2 + 5√3
= 7√3 + 12√2