Download 9.2

Chapter 9 - Radical Functions
Mini-Lesson
Section 9.2 – Operations with Radical Expressions
!
Operations on radical expressions work the same way as operations on polynomial
expressions.
When multiplying two monomial expressions, you multiply like factors, that is, you multiply
coefficients together and variables together. Similarly, when multiplying two monomial
radicals, you multiply the numbers outside the radical sign together and the radicands together,
M
M
as long as the radicals have the same index. To multiply radicands, we use the rule: N ∙ ; =
M
N ∙ ;. (Note: When n is even, this rule works only for positive radicands.)
!
Problem 7
WORKED EXAMPLE – Multiplying Radicals
!
Multiply the following. Be sure to simplify all answers.
15 ⋅ 10
a)
15 ⋅ 10 = 150
= 25 ⋅ 6
Multiply the two radicands using
Simplify
=5 6
b)
4 3 2 ⋅ 7 3 20
4 3 2 ⋅ 7 3 20 = 28 3 40
= 28 3 8 ⋅ 5
Multiply the two radicands using
Simplify
= 28 ⋅ 2 3 5
= 56 3 5
!
YOU TRY – Multiplying Radicals
Problem 8
!
Multiply the following. Be sure to simplify all answers.
d
d
a) 3 2 ∙ 5 2
b) 2 12 ∙ 4 6
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Chapter 9 - Radical Functions
Mini-Lesson
When adding or subtracting polynomial expressions, you add and subtract coefficients whose
variable and its exponent are alike. Similarly, when adding or subtracting radical expression,
you add and subtract the number outside the radical sign as long as the radical expression’s index
and radicand are alike.
!
Problem 9
WORKED EXAMPLE – Multiplying Radicals
!
Use the distributive property to multiply the following radicals. Simplify all answers.
a)
6
(
2 −7
6
(
)
)
2 − 7 = 12 − 7 6
= 4⋅3 − 7 6
= 2 3−7 6
b)
( 3 + 8)( 15 − 2)
(
3 +8
)( 15 − 2) =
45 − 2 3 + 8 15 − 16
= 9 ⋅ 5 − 2 3 + 8 15 − 16
= 3 5 − 2 3 + 8 15 − 16
c)
2
(10 + 5 )
2
(10 + 5 ) = (10 + 5 )(10 + 5 )
= 100 + 10 5 + 10 5 + 25
= 100 + 20 5 + 5
= 105 + 20 5
d)
(8 − 7 )(8 + 7 )
(8 − 7 )(8 + 7 ) = 64 + 8
7 − 8 7 − 49
= 64 − 7
= 57
!
!
!
355
Chapter 9 - Radical Functions
Problem 10
Mini-Lesson
MEDIA/CLASS EXAMPLE – Multiplying Radicals
Use the distributive property to multiply the following radicals. Simplify all answers.
( 2 + 6) !
b)
( 7 + 1)( 2 − 5)!
(6 + 15 ) !
d)
(4 − 3 )(4 + 3 ) !
a)! 8
!
!
!
!
!
!
!
!
c)
2
Problem 11
YOU TRY – Multiplying Radicals
!
Multiply the following. Be sure to simplify your answers.
(
(
)
b)
3 15 + 8
(
)
d)
2
a)
6 2− 5
c)
3 8 + 27
)
( 6 − 12)
356
Chapter 9 - Radical Functions
Problem 12
Mini-Lesson
YOU TRY – Multiplying Radicals
Multiply the following. Be sure to simplify your answers.
a)
( 5 + 7)( 5 − 2)
b)
( 18 − 5)( 2 + 8)
c)
( 5 − 5)( 10 − 4)
d)
(9 + 14 )( 2 − 9)
f)
(
(
)
(
)(
e) 4 + 13
2
g) 2 + 19 2 − 19
)
(
5 −6
)
2
)(
h) 10 + 8 10 − 8
)
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