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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. 1. To Multiply Radical Expressions. 7-2. Multiplying and Dividing Radical Expressions. ALGEBRA 2 LESSON 7-2. - PowerPoint PPT Presentation
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Algebra 2Lesson 7-2(Page 368)
ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions
7-2
To Multiply Radical Expressions
ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions
7-2
If and are real numbers,
Then .
ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions
7-2
n a n b
n n na b ab
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiply. Simplify if possible.
b. –16 • 4
a. 3 • 12
3 • 12 = 3 • 12 = 36 = 6
The property for multiplying radicals does not apply. –4 is not a real number.
c. –4 • 16
3 3
7-2
3 333–16 • 4 = –16 • 4 = 64 = –4
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiply. Simplify if possible.
7-2
. 3 12a 3 3. 3 9b 4 4. 4 4c
a. 6 b. c. 36 d.
a. –3 b. 3 c. not possible d. 27
a. 4 b. –4 c. not possible d. 2
a. 50x5
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Simplify each expression. Assume all variables are positive.
= 5x2 2x definition of nth root
Factor into perfect squares.50x5 = 52 • 2 • (x2)2 • x
3b. 54n8
33 54n8 = 33 • 2 • (n2)3 • n2 Factor into perfect cubes.
3= 3n2 2n2 definition of nth root
7-2
33= 33(n2)3 • 2n2 n n na • b = ab
= 52 • (x2)2 • 2 • x n n na • b = ab
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Simplify each expression. Assume all variables are positive.
7-2
a. b. c. d.
4. 50a x 3 4. 18b x
a. b. c. d.
33 25xy8 • 5x4y3
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiply and simplify . Assume all variables
are positive.
3= 53x3(y3)3 • x2y2 Factor into perfect cubes.
3= 5xy3 x2y2 definition of nth root
7-2
3 3= 53x3(y3)3 • x2y2 n n na • b = ab
25xy8 • 5x4y3 = 25xy8 • 5x4y33 3 3 n n na • b = ab
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiply and simplify
Assume all variables are positive.
7-2
3 3 23 7 2 21x x y
a. b. c. 66x 3 y d. 42xy
To Divide Radical Expressions
ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions
7-2
If and are real numbers,
and ,
then .
ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions
7-2
n a n b
n
nn
a a
bb
0b
3= 64x7
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Divide and simplify. Assume all variables are positive.
a.
3= –27
3= (–3)3
= –3
3 –81
33=
b.
3x3
3 192x8
=
192x8
3x
3
=
= 4x2 x3
3= 43(x2)3 • x
7-2
=3 –81
3
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Divide and simplify. Assume all variables are positive.
7-2
To of
an expression, rewrite it so there are no
Radicals in any denominators.
ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions
7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Rationalize the denominator of each expression. Assume that
all variables are positive.
155=
a.
5
3
7-2
Method 1:
Rewrite as a square root of a fraction.
35
=5
3
= 3 • 55 • 5
Then make the denominator a perfect square.
= 1552
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
(continued)
3 • 55 • 5
Multiply the numerator and denominator by 5 so the denominator becomes a whole number.
=3
5
Method 2:
a.
155=
7-2
5
3
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
(continued)
b. x5
3x2y
c. 3 54y
x5
3x2y
x5 3x2y
3x2y3x2y
•
•=
3x7y3x2y
=
x3 3xy3x2y
=
x 3xy3y
=
3 5 • 42y2
4y • 42y2
3 54y
=
Rewrite the fraction so the denominator is a perfect cube.
3 80y2
43y3=
2 10y2
4y3
=
10y2
2y
3=
7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 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
t 2 =d
4.9
t =d
4.9
10d7
=
d • 1049=
7-2
Algebra 2Lesson 7-2(Page 368)
ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2
Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions
7-2