Verified answer

3 x (-1/√3)²

--> 3 x (1/3) [(-1/√3)² means (-1/√3) x (-1/√3), that is, negative multiplied to negative, which gives answer as positive.]

--> 1

Depends if you want it to. Ultimately, it doesn't matter, however.

Say I have this:

-1 / sqrt(3)

I can also write it like this:

1 / -sqrt(3)

These are equivalent things as long as I don't use the negative sign twice.

But to show why it doesn't matter in this particular example, let me write it like this:

(-1) * (1/sqrt(3))

Then you square that:

[(-1) * (1/sqrt(3))]^2

(-1)^2 * (1/sqrt(3))^2

1 * 1/3

1/3

See? The negative sign went away. Squaring a negative number will always result in a positive number.

If you then multiply that by 3, you get 1.

The sign is not applied to either 1 or √3, but rather the whole thing. It can go either to the 1 or the √3, you will still get the same answer.

Yes

It won't