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 = 1and 2^2 = 4. This means that \sqrt{2} is somewhere between 1 and 4. What about \sqrt{5}» Read more