Question

How do you simplify `sqrtt*sqrtt`?

Answer 1

`|t|`

Explanation:

We can multiply these together like this:

`sqrtt * sqrtt = sqrt(t*t) = sqrt(t^2)`

You might feel inclined to say that `sqrt(t^2) = t`, but notice that if `t` is negative, `t^2` is still positive, and so the square root of `t^2` will be positive `-` that is, the absolute value of `t`.

No matter what, `sqrt(t^2)` will always be positive (or `0`) since any number squared is non-negative. Therefore, we can say that:

`sqrtt * sqrtt = sqrt(t^2) = |t|`

Final Answer