Download Multiplying/Dividing Radical Expressions (7-2)

Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Algebra 2
Lesson 7-2
(Page 368)
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
To Multiply Radical Expressions
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
If n a and n b are real numbers,
Then n a  n b  n ab .
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Multiply. Simplify if possible.
a.
b.
c.
3•
12
3•
12 =
3
–16 •
3
4
3
–16 •
3
4=
–4 •
16
3 • 12 =
3
36 = 6
–16 • 4 =
3
64 = –4
The property for multiplying radicals does not apply.
–4 is not a real number.
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Multiply. Simplify if possible.
a. 3  12
a. 6
b.
c. 36
d.
b. 3 3  3 9
a. –3
b. 3
c. not possible
d. 27
7-2
c. 4 4  4 4
a. 4
b. –4
c. not possible
d. 2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Simplify each expression. Assume all variables are positive.
50x5
a.
50x5 =
=
52 • 2 • (x2)2 • x
Factor into perfect squares.
52 • (x2)2 •
n
= 5x2
b.
2•x
2x
54n8
3
54n8 =
3
33 • 2 • (n2)3 • n2
=
3
33(n2)3 •
3
2n2
n
b =
n
ab
definition of nth root
3
= 3n2
a•
3
2n2
Factor into perfect cubes.
n
a•
n
b =
n
ab
definition of nth root
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Simplify each expression. Assume all variables are positive.
a. 50 x 4
b. 3 18 x 4
a.
b.
c.
d.
a.
b.
c.
d.
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Multiply and simplify
are positive.
3
25xy8 •
3
3
25xy8 • 5x4y3
=
3
53x3(y3)3 • x2y2
=
3
53x3(y3)3 •
= 5xy3
3
25xy8 •
n
5x4y3 =
3
3
a•
3
n
5x4y3 . Assume all variables
b =
n
ab
Factor into perfect cubes.
x2y2
x2y2
n
a•
n
b =
n
ab
definition of nth root
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Multiply and simplify 3 7 x  2
Assume all variables are positive.
3
a.
b.
c. 66x 3 y
d. 42xy
7-2
21x3 y 2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
To Divide Radical Expressions
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
If n a and n b are real numbers,
and b  0 ,
then
.
n
a
a
n


n
b
b
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Divide and simplify. Assume all variables are positive.
a.
3
=
=
–81
3
3
b.
3
3
=
–81
3
=
192x8
3
3
3x
192x8
3x
=
3
–27
=
3
64x7
=
3
(–3)3
=
3
43(x2)3 • x
= –3
= 4x2
7-2
3
x
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Divide and simplify. Assume all variables are positive.
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
To
of
an expression, rewrite it so there are no
Radicals in any denominators.
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Rationalize the denominator of each expression. Assume that
all variables are positive.
Method 1:
a.
3
3
5
5
=
3
5
Rewrite as a square root of
a fraction.
=
3•5
5•5
Then make the denominator
a perfect square.
=
15
52
=
15
5
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
(continued)
Method 2:
a.
3
3
5
5
=
3•
5•
=
15
5
5
5
Multiply the numerator and
denominator by 5 so the denominator
becomes a whole number.
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
(continued)
b.
c.
x5
3
5
4y
3
5
4y
3x2y
x5
3x2y
=
=
=
=
x5 •
3x2y
3x2y •
3x2y
3x7y
3x2y
x3
x
3xy
2
3x y
=
3
5 • 42y2
4y • 42y2
=
3
80y2
=
3xy
3y
=
7-2
43y3
2
3 10y2
4y
3 10y2
2y
Rewrite the fraction
so the denominator
is a perfect cube.
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
The distance d in meters that an object will fall in t seconds is
given by d = 4.9t 2. Express t in terms of d and rationalize the
denominator.
d = 4.9t 2
d
t 2 = 4.9
t=
=
=
d
4.9
d • 10
49
10d
7
7-2
Multiplying and Dividing Radical Expressions
ALGEBRA 2 LESSON 7-2
Algebra 2
Lesson 7-2
(Page 368)
7-2