## 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 $\sqrt{4}$. From the discussion above, we now know that

$\sqrt{4} = 2$.

It is easy to see that $\sqrt{1} = 1$, since $1^2 = 1$ and $\sqrt{0} = 0$ since $0^2 = 0$.

The square root of the two numbers above are integers, but this is not always the case. For instance, $\sqrt{2}$ is clearly not an integer since $1^2 = 1$and $2^2 = 4$. This means that $\sqrt{2}$ is somewhere between 1 and 4. What about $\sqrt{5}$» Read more