**Notes on Square Roots**

Since a square has four congruent sides, to find the area of a square you multiply a side by itself.

In other words area = side^{2}.

To find the length of a side of a square when you know the
area, you must find the square root.
What number multiplied by itself will give you the area?

For example: 8^{2}=64 so the square root is _{}=8 (notice the symbol
for square root)

Every **square root** has **two** solutions, a **negative**
one and a **positive** one:

_{}=8 and_{}= -8

If you want the negative solution then you would write -_{}= -8, otherwise you will have two solutions.

The positive solution is called the **principal** **square root**.

A **perfect square** is a
number that is the square of a **whole** number. For example the number 25 is a perfect square
because its square roots are integers.

Perfect squares are **rational**
numbers.

Numbers such as _{} and .36 also have two
roots; they are also perfect squares.

_{}= _{}or -_{} and _{}= .6 and -.6
These are also **rational** numbers.

The number 0 has only one square root: _{}=0.

The square root of any rational number that is **not** a
perfect square is a **nonterminating**,
**nonrepeating**
decimal. This type of decimal is called
an **irrational** number.

For example: _{}= 3.162 approximately (this is rounded to the nearest
thousandth). This is an irrational
number