radical questions or is it extraneous?

Question

1. sqrt.[5x-6]=2
2. 3+sqrt[x+7]=sqrt[x+4]
3. 3+sqrt[x]=sqrt[x-3]
4. sqrt[x-5]-sqrt[x-3]=4
5. sqrt[x+2]=sqrt[4-x]
6. sqrt[x+2]-sqrt[6x]=-1
7. 2x=sqrt[12x-5]
8. 2+sqrt[x]=sqrt[x+4]

Answer 1

Is the problem that you have to solve these for x? If so, which have you already done?

Some are clearly trivial. For example, square both sides of #5 to get:
x+2 = 4-x

As for equations such as #2, square both sides to get:
9 + (x+7) + 6sqrt(x+7) = x + 4

let u = sqrt(x+7) so u^2 = x + 7 or x = u^2 - 7
substitute to get:
9 + u^2 + 6u = 4 - (u^2 - 7)

This is a quadratic in u so you can solve it. Then you can compute u^2 and then x.