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In this chapter, we explore rational exponents and radicals, focusing on the concept of nth roots. The symbol n√ indicates the nth root, where n represents the index. We'll discover how to identify the radicand, the number under the radical sign, and discuss different cases based on whether a is nonnegative or negative. Key points include the behavior of nth roots for positive, negative, and even or odd indices, as well as simplifying radical expressions involving variables using power rules. Follow along to enhance your understanding of radical expressions and functions!
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Chapter Eight Rational Exponents and Radicals
Section 8.1 Radical Expressions and Functions
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
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
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!
