A square has area of 392 . What is the side length of the square?

So, we have a square with an area of 392, and we want to find the side length.

The first thing we have to ask ourselves is the question, "what is a square?"

Thinking about it, the definition is "a shape that has four sides that are all the same size, and has right angles in each corner"

With that out of the way, we can realize how to find the area of a square from its side lengths: multiplication, in this case an operation aptly called "squaring".

By multiplying two perpindicular sides (represented by s) of the square, we arrive at the area (represented by a):

$s \times s = a$, also represented as ${s}^{2} = a$

Since we know what the area is, 392, we can substitute that for a:

${s}^{2} = a$

${s}^{2} = 392$

Then to cancle the "squared" operation, a square root is used:

$\sqrt{s^2} = \sqrt{392}$

$s = \sqrt{392}$

And there is the answer. The length of a side is $\sqrt{392}$, which is approximately 19.7989898732233307