# How do you simplify sqrt t * sqrt t?

##### 1 Answer
Sep 7, 2015

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

#### Explanation:

$\sqrt{t} \cdot \sqrt{t} = {\left(\sqrt{t}\right)}^{2} = t$ by definition of square root.

A square root of $t$ is a number which when multiplied by itself (i.e. squared) gives $t$

On the other hand, be careful with the expression $\sqrt{{t}^{2}}$. This is not always equal to $t$.

If $t \in \mathbb{R}$ then $\sqrt{{t}^{2}} = \left\mid t \right\mid$