## The Algebra and Geometry of Square Root

If we have a square with a given area, then we can find the length of its side. For example, a square with area 4 square units has a side length of 2 units. In other words, in finding the side length of a square with area 4 square units,we are looking for a number that is equal to 4 when squared.The number that when squared is equal to 4 is called the **square root of 4** and is written as . From the discussion above, we now know that

.

It is easy to see that , since and since .

The square root of the two numbers above are integers, but this is not always the case. For instance, is clearly not an integer since and . This means that is somewhere between 1 and 4. What about ? » Read more