Question

How do you simplify `-sqrt(144)`?

Answer 1

The negative is really -1 times the square root, so do the square root first, multiply by -1 and get
`(-1)(12)=-12`

Explanation:

Let's start with the original:

`-sqrt144`

The negative sign is really a `-1` multiplying the square root, so let's write the expression this way:

`(-1)(sqrt144)`

We can now take the square root of 144:

`(-1)(12)=-12`

I think this question hinged on the fact that "you can't take the square root of a negative number" (which in a higher level class you will learn that you can). A question with the negative in the square root would look like this:

`sqrt(-144)`

And just for fun let's show what you do in this case:

`sqrt(-144)=sqrt(144)sqrt(-1)=12sqrt(-1)`

And in that advanced class you will learn that `sqrt(-1)=i`, so the answer becomes

`sqrt(-144)=sqrt(144)sqrt(-1)=12sqrt(-1)=12i`