Algebra: Chapter 11-5, p 498
Dividing and Simplifying
The `sqrt` of quotients is pretty simple. You can combine or break apart quotient `sqrt`s to your liking.
Try to find perfect squares and make sure that all the factors are simplified.
Division Property for Radicals:
`sqrt(a/b) = sqrt(a)/sqrt(b)` Remember too, that you can go back and forth without any problem.
Remember too, to “rationalize the denominator”. Make sure that NO radical appears in the denominator. If you have one, multiply the numerator and denominator by 1 (the `sqrt` of the denominator) to make it disappear. The `sqrt(a) * sqrt(a) = sqrt(a^2) = a`!
An expression containing radicals is simplified when the following conditions are met:
- The radicand contains NO perfect square factors
- A fraction in simplest form does not have a radical in the denominator
- A simplified radical does not contain a fractional radicand.
For example:
`sqrt(2)/sqrt(3) = sqrt(2)/sqrt(3) * sqrt(3)/sqrt(3)`
`= [sqrt(2) * sqrt(3)] / [sqrt(3) * sqrt(3)]`
`= sqrt(6)/3 = [1/3] * sqrt(6)`
See this link from purplemath.com.
Math-8: Chapter 11-8, p 589
Polygons
Polygons are simple, closed sided figures (in a plane) that are formed with at least 3 line segments. The points of intersection are called the vertices (the plural of vertex).
A diagonal is a line segment that joins 2 NONCONSECUTIVE (not right next to each other) vertices. You can draw diagonals in any polygon with more than 3 sides.
If a polygon has `n` sides, the `n – 2` triangles are formed and the sum of the degree measures of the interior angles of the polygon is `(n – 2) * 180°`