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
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)
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