5-6
Radical Expressions and Rational Exponents
Warm Up
Simplify each expression.
1. 73 • 72
2.
118
116
3. (32)3
4. 75
5.
20
7
Holt McDougal Algebra 2
5-6
Radical Expressions and Rational Exponents
Objectives
Rewrite radical expressions by using rational
exponents.
Simplify and evaluate radical expressions and
expressions containing rational exponents.
Vocabulary
index
rational exponent
Holt McDougal Algebra 2
5-6
Radical Expressions and Rational Exponents
The nth root of a real number a can be written as
the radical expression
, where n is the index
(plural: indices) of the radical and a is the radicand.
When a number has more than one root, the radical
sign indicates only the principal, or positive, root.
Reading Math
When a radical sign shows no index, it represents
a square root.
Holt McDougal Algebra 2
5-6
Radical Expressions and Rational Exponents
Example 1: Finding Real Roots
Find all real roots.
A. sixth roots of 64
B. cube roots of –216
C. fourth roots of –1024
Holt McDougal Algebra 2
5-6
Radical Expressions and Rational Exponents
The properties of square roots also apply to nth
roots.
Remember!
When an expression contains a radical in the
denominator, you must rationalize the
denominator. To do so, rewrite the expression so
that the denominator contains no radicals.
Holt McDougal Algebra 2
5-6
Radical Expressions and Rational Exponents
Example 2: Simplifying Radical Expressions
Simplify each expression. Assume that all
variables are positive.
3
Holt McDougal Algebra 2
x7
3
x2
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Radical Expressions and Rational Exponents
A rational exponent is an exponent that can be
expressed as m , where m and n are integers and
n
n ≠ 0. Radical expressions can be written by using
rational exponents.
Writing Math
The denominator of a rational exponent becomes
the index of the radical.
Holt McDougal Algebra 2
5-6
Radical Expressions and Rational Exponents
Example 3: Writing Expressions in Radical Form
3
5
Write the expression (–32) in radical form
and simplify.
Holt McDougal Algebra 2
5-6
Radical Expressions and Rational Exponents
Example 4: Writing Expressions by Using Rational
Exponents
Write each expression by using rational
exponents.
A.
Holt McDougal Algebra 2
B.
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Radical Expressions and Rational Exponents
Rational exponents have the same properties as
integer exponents
Holt McDougal Algebra 2
5-6
Radical Expressions and Rational Exponents
Example 5: Simplifying Expressions with Rational
Exponents
Simplify each expression.
Holt McDougal Algebra 2
5-6
Radical Expressions and Rational Exponents
Example 6: Chemistry Application
Radium-226 is a form of radioactive element that decays
over time. An initial sample of radium-226 has a mass of
500 mg. The mass of radium-226 remaining from the
initial sample after t years is given by
. To the
nearest milligram, how much radium-226 would be left
after 800 years?
Pg 363 30-71, 85-88
Holt McDougal Algebra 2