Lesson 31 – Simplifying Radical Expressions

Math 2 Honors - Santowski

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FAST FIVE Evaluate each expression if p = 4 and q = -3

pqC

pB

pqA

6 :

q6 :

36 : 2

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Opening Investigation Prepare a table of values and then graph the

following “functions”

2

3 3

44

( )

( )

( )

f x x

g x x

h x x

l x x

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Opening Investigation Given the functions you have investigated,

what is true about the “algebraic operations” (THINK: input & output) defined by

( ) n nh x x

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Opening Investigation Simplify the following expressions:

2

2

2

2

25

)5(

)5(

x

x

4

4

4

4

625

)5(

)5(

x

x

4 4

4 4

4 4

4

625

)5(

625

x

x

3 3

3 3

3 3

3

125

)5(

125

x

x

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(A) Terminology Associated with Radicals

Index of the radical Radical sign Radicand

Simplest form

Mixed radicals

Entire radicals

n x

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(B) Simplest Form

Simplify:

4 63 24 24

5 24 323 2

43

34

36 (p) (o) 2 (n) 2 (m)

(l) (k) (j) 2 (i)

2

3 (h)

4

7 (g)

2

25 (f)

5

3 (e)

54 (d) 48 (c) 27 (b) 3 (a)

xy

yxyxaa

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(C) Simplifying Radicals with Variables

Simplify the following:

Simplify the following:

535725

642

81 (f) 49 (e) 36 (d)

36 (c) 36 (b) 36 (a)

yxyxyx

yyx

34 586 13

6 75 33 5

72x-(f) 16 (e) 64y (d)

128 (c) 64y (b) 125 (a)

qp

xx

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(D) Operations With Radicals – Add & Subtract In order to add and subtract with radicals, the

(a) indices must by the same and (ii) the radicands must be “alike”

Simplify the following:

bbbab 4447 (d)

5832051353402 (c)

27323518122 (b)

55365234 (a)

223

3333

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(E) Operations with Radicals: Multiply and Divide

T or F

T or F

T or F

T or F

baba ?

abba?

?nnn abba

b

aba

?

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(E) Operations with Radicals: Multiply and Divide Simplify the following:

23

2233 (h)

12

1 (g)

81

3a- (f) 28 (e)

416 (d) 235253 (c)

253352 (b) 12283 (a)

3

3 974 34 4

3 2

a

baab

aa

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(F) Homework

p. 533 # 15-91 every other odd

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