# How do you simplify sqrtt*sqrtt?

Jul 11, 2017

$| t |$

#### Explanation:

We can multiply these together like this:

$\sqrt{t} \cdot \sqrt{t} = \sqrt{t \cdot t} = \sqrt{{t}^{2}}$

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:

$\sqrt{t} \cdot \sqrt{t} = \sqrt{{t}^{2}} = | t |$