1. Rational Exponents and Radicals
Chapter Eight
Rational Exponents and Radicals

2. Radical Expressions and Functions
Section 8.1
Radical Expressions and Functions

3. Finding nth Roots Symbol: n√ n represents the index of the root.
The value under the symbol is called the radicand.
The nth root of a number a is the value that when raised to the nth = a

4. Possible Outcomes for n√a
If a is nonnegative, then n√a = b
where b > 0 and bn = a
If a is negative and n is even, there is no real number root.
If a is negative and n is odd, then n√a = b
where b is negative and bn = a

5. Simplify Radical Expressions
When variables are part of the radicand, recall the rules for raising a power to a power…
(xm)n = xmn
Note: the radicand must not be negative if the root index is even. To ensure this with radicands that include real number variables, use absolute value notation!