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)

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

To simplify the expression sqrt12 - sqrt18 + 3sqrt50 + sqrt75, we can start by breaking down each term into its prime factors.

sqrt12 = sqrt(2^2 * 3) = 2sqrt3
sqrt18 = sqrt(2 * 3^2) = 3sqrt2
3sqrt50 = 3sqrt(2 * 5^2) = 3 * 5sqrt2 = 15sqrt2
sqrt75 = sqrt(3 * 5^2) = 5sqrt3

Now we can substitute these simplified terms back into the original expression:

sqrt12 - sqrt18 + 3sqrt50 + sqrt75
= 2sqrt3 - 3sqrt2 + 15sqrt2 + 5sqrt3

Combining like terms:

= (2sqrt3 + 5sqrt3) + (-3sqrt2 + 15sqrt2)
= 7sqrt3 + 12sqrt2

Therefore, the simplified form of the expression sqrt12 - sqrt18 + 3sqrt50 + sqrt75 is 7sqrt3 + 12sqrt2.