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Chapter 8
Rational Exponents, Radicals,
and Complex Numbers
Active Learning
Questions
© 2011 Pearson Prentice Hall.
All rights reserved
3-1
Section 7.1
Radicals and Radical Functions
Identify the domain of f (x)  3 x  5.
a.) [0, ∞)
b.) (– ∞, ∞)
c.) [5, ∞)
© 2011 Pearson Prentice Hall. All rights reserved
3-2
Section 7.1
Radicals and Radical Functions
Identify the domain of f (x)  3 x  5.
a.) [0, ∞)
b.) (– ∞, ∞)
c.) [5, ∞)
© 2011 Pearson Prentice Hall. All rights reserved
3-3
Section 7.1
Radicals and Radical Functions
Which one is not a real number?
a.)
3
15
b.)
4
15
c.)
5
15
© 2011 Pearson Prentice Hall. All rights reserved
3-4
Section 7.1
Radicals and Radical Functions
Which one is not a real number?
a.)
3
15
b.)
4
15
c.)
5
15
© 2011 Pearson Prentice Hall. All rights reserved
3-5
Section 7.2
Rational Exponents
Simplify: x  x
4
1
2
a.) x 2
b.) x
c.) x
5
9
2
2
© 2011 Pearson Prentice Hall. All rights reserved
3-6
Section 7.2
Rational Exponents
Simplify: x  x
4
1
2
a.) x 2
b.) x
c.) x
5
9
2
2
© 2011 Pearson Prentice Hall. All rights reserved
3-7
Section 7.2
Rational Exponents
Which one is correct?
2
a.) 8
b.) 8
2
c.) 8
3
1

4
3
 4
2
3
1

4
© 2011 Pearson Prentice Hall. All rights reserved
3-8
Section 7.2
Rational Exponents
Which one is correct?
2
a.) 8
b.) 8
2
c.) 8
3
1

4
3
 4
2
3
1

4
© 2011 Pearson Prentice Hall. All rights reserved
3-9
Section 7.3
Simplifying Radical Expressions
3
Find and correct the error:
27 3 27 3

 3
9
9
3
a.)
27
3
9
3
27 3
 1
9 3
3
27 3 27

3
9
9
b.)
c.)
© 2011 Pearson Prentice Hall. All rights reserved
3-10
Section 7.3
Simplifying Radical Expressions
3
Find and correct the error:
27 3 27 3

 3
9
9
3
a.)
27
3
9
3
27 3
 1
9 3
3
27 3 27

3
9
9
b.)
c.)
© 2011 Pearson Prentice Hall. All rights reserved
3-11
Section 7.4
Adding, Subtracting, and
Multiplying Radical Expressions
Which is true?
a.)
b.)
5  7  12
3
3
3
3
5  7  35
3
3
3
c.)
7 3
 2
3
5
© 2011 Pearson Prentice Hall. All rights reserved
3-12
Section 7.4
Adding, Subtracting, and
Multiplying Radical Expressions
Which is true?
a.)
b.)
5  7  12
3
3
3
3
5  7  35
3
3
3
c.)
7 3
 2
3
5
© 2011 Pearson Prentice Hall. All rights reserved
3-13
Section 7.4
Adding, Subtracting, and
Multiplying Radical Expressions
True or false?
a  b  ab
a.) True
b.) False
c.) Sometimes true
© 2011 Pearson Prentice Hall. All rights reserved
3-14
Section 7.4
Adding, Subtracting, and
Multiplying Radical Expressions
True or false?
a  b  ab
a.) True
b.) False
c.) Sometimes true
© 2011 Pearson Prentice Hall. All rights reserved
3-15
Section 7.5
Rationalizing Numerators and
Denominators of Radical Expressions
3
To rationalize the denominator of 3 7 ,
5
multiply by what form of 1?
3
5
a.) 3
5
3
7
b.) 3
7
3
25
c.) 3
25
© 2011 Pearson Prentice Hall. All rights reserved
3-16
Section 7.5
Rationalizing Numerators and
Denominators of Radical Expressions
3
To rationalize the denominator of 3 7 ,
5
multiply by what form of 1?
3
5
a.) 3
5
3
7
b.) 3
7
3
25
c.) 3
25
© 2011 Pearson Prentice Hall. All rights reserved
3-17
Section 7.5
Rationalizing Numerators and
Denominators of Radical Expressions
Determine by which number the numerator and
denominator can be multiplied by to rationalize
1
the denominator of 4 .
8
a.) 4 4
b.)
c.)
4
4
2
8
© 2011 Pearson Prentice Hall. All rights reserved
3-18
Section 7.5
Rationalizing Numerators and
Denominators of Radical Expressions
Determine by which number the numerator and
denominator can be multiplied by to rationalize
1
the denominator of 4 .
8
a.) 4 4
b.)
c.)
4
4
2
8
© 2011 Pearson Prentice Hall. All rights reserved
3-19
Section 7.6
Radical Equations and Problem Solving
Choose the next step to solve:
x3 x  2
a.)

x3  x  2
2
x3  x2
b.)
c.)

2


2
x3  x  2
2
2
© 2011 Pearson Prentice Hall. All rights reserved
3-20
Section 7.6
Radical Equations and Problem Solving
Choose the next step to solve:
x3 x  2
a.)

x3  x  2
2
x3  x2
b.)
c.)

2


2
x3  x  2
2
2
© 2011 Pearson Prentice Hall. All rights reserved
3-21
Section 7.6
Radical Equations and Problem Solving
How can you immediately tell that the equation
2 y  3  4 has no real solution?
a.) The square root of a number is never negative.
b.) You cannot take the square root of a variable.
c.) 2y + 3 equals 0.
© 2011 Pearson Prentice Hall. All rights reserved
3-22
Section 7.6
Radical Equations and Problem Solving
How can you immediately tell that the equation
2 y  3  4 has no real solution?
a.) The square root of a number is never negative.
b.) You cannot take the square root of a variable.
c.) 2y + 3 equals 0.
© 2011 Pearson Prentice Hall. All rights reserved
3-23
Section 7.7
Complex Numbers
True of false? Every complex number is also a
real number.
a.) True
b.) False
c.) Sometimes true
© 2011 Pearson Prentice Hall. All rights reserved
3-24
Section 7.7
Complex Numbers
True of false? Every complex number is also a
real number.
a.) True
b.) False
c.) Sometimes true
© 2011 Pearson Prentice Hall. All rights reserved
3-25