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
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