Back to Unit 14

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 = side2.

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: 82=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.  Some perfect squares are not whole numbers.

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