Algebra: Chapter 11, Lesson 1 and Lesson 2, page 482 and page 487.
Real Numbers (Square Roots) and Radical Expressions
Definition: the number `c` is a square root of `a` if `c^2=a`. In math symbols then, `c = sqrt(a^2)`
Prinicipal square root is the positive square root of a number, like `sqrt(36)=6`
Real numbers have 2 sets, the rational numbers and the irrational numbers.
- Rational number can be expressed as a ratio of 2 integers. They can have a repeating decimal AS LONG AS THERE IS A PATTERN.
- Irrational numbers conversely, cannot be expressed as a ratio or have a repeating decimal WITH NO PATTERN. The best irrational number example is π.
We, in Algebra 1, cannot take the square root of a negative numbers. By definition, then all RADICANDS, the thing under the square root symbol, MUST always be positive.
An expression written under the radical is also called a radical expression. With the exception of perfect square numbers (0, 2, 4, 9, 16, 25, 36, 49, 64, 81, 100 …) most square roots of whole numbers are irrational.
Finally, the `sqrt(a^2)` can be simplified to `| a |`, this gives up 2 values for the square root, a positive and negative value.
Here again is a great link from Purplemath.