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Simplifying Radical Expressions: Rules and Examples

Understand radical expressions with variables, nth roots, and simplification rules. Learn how to handle negative radicands and exponents effectively.

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Simplifying Radical Expressions: Rules and Examples

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  1. Chapter Eight Rational Exponents and Radicals

  2. Section 8.1 Radical Expressions and Functions

  3. Finding nth Roots • Symbol: n√ • n represents the indexof 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!

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