**Elementary
Algebra Chapter 8
Roots and Radicals**

**From
Section 8.1, 8.2, and 8.3
Definition: **A number b
is a

**FACT:**
Every positive number has two square roots, one that is positive and one that
is negative.

**Definition:
** The **principal
square root** of a number is its positive square root. The principale
square root of 0 is 0.

**FACT:
**The
square root of a negative number is not a real number.

**The
Pythagorean Theorem:** If
the length of the hypotenuse of a right triangle is c and the lengths of its
legs are a and b, then a^{2} + b^{2} = c^{2}

**Definition:
**A number b is a **cube
root** of a if b^{3} = a

**Definition:
** A
number b is the n^{th} root of
a if b^{n} = a.