Question

How do you simplify `sqrt(3x^2 - 12x + 12)`?

Answer 1

`sqrt(3x^2-12x+12) = sqrt(3)*abs(x-2)`

Explanation:

When `a, b >= 0` we have `sqrt(ab) = sqrt(a)sqrt(b)`

`sqrt(3x^2-12x+12)`

`=sqrt(3*(x^2-4x+4))`

`=sqrt(3*(x-2)^2)`

Now `3 >= 0` and `(x-2)^2 >= 0` for all `x in RR`

So:

`sqrt(3*(x-2)^2)`

`= sqrt(3)*sqrt((x-2)^2)`

`= sqrt(3)*abs(x-2)`

Note that `(x-2)^2` has two square roots, namely `(x-2)` and `-(x-2)`.

`sqrt((x-2)^2)` denotes the positive square root, so we have to pick the positive value from `(x-2)` and `-(x-2)`, which we can do by using `abs(x-2)`