1. Example 1: Finding Real Roots
8-6 LEARNING GOALS
Rewrite radical expressions by using rational exponents.
Simplify and evaluate radical expressions and expressions
containing rational exponents.
The nth root of a real number a can be written as the radical expression:
__________ is the index (plural: indices)
* If the index is left blank it means the index = ________
__________ is the radicand n a
Example 1: Finding Real Roots
Find all real roots.
A. sixth roots of 64
B. cube roots of –216
C. fourth roots of –1024
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2. Example 2: Writing Expressions in Radical Form
Write the expression in radical form and simplify.
Method 1 Evaluate the root first.
Method 2 Evaluate the power first.
Use a calculator.
A __________ ____________is an exponent that can be expressed as
For example:
Write the expression in radical form, and simplify.
A. 64⅓
B. 45/2
C ¾
Example 3: Writing Expressions by Using Rational Exponents
Write each expression by using rational exponents. A. B.
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3. Example 4: Simplifying Expressions with Rational Exponents
Simplify each expression. Check with your calculator. A. B. C. D. E. F.
Example 5: Simplifying Radical Expressions
Simplify each expression. Assume that all variables are positive.
A. B. C.
D. E. F.
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4. Example 5: Simplifying Radical Expressions
Simplify each expression. Assume that all variables are positive. A. B. C. D. E.
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5. Example 5: Simplifying Radical Expressions
Simplify each expression. Assume that all variables are positive. A. B. C. D. E. F.
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