aim: multiply & divide radicals course: adv. alg. & trig. aim: how do we multiply and divide...
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Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.
Aim: How do we multiply and divide radicals?
Do Now:
)4)(2( 32 xx
xa • xb = xa + b
))()(4)(2( 32 xx532 88 xx
Divide:
2
35
12
3648
x
xx
xa xb = xa - b
34x x3
Multiply:
Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.
Multiplying Radicals
Multiplying
•Multiply the radicands
4085. ex
•If there are coefficients, find their product, and combine the result with the radical product.
n n nx a y b xy ab
26532563. ex
1215 3303415
n n na b a b rule #1
Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.
Dividing Radicals
Dividing•Divide the radicands
398
72
8
72. ex
•If there are coefficients, find their quotient, and combine the result with the quotient of the radicands. Simplify.
n
nn
x a x a
y by b
n
nn
a a
bb
rule #2
Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.
Model Problems
Simplify:
16
424
4
16
18 96
3 54
22
4
4
16
Note:
616 6
9 6
64 6
3 6
82
16 125 8 5
16
8
125
5
2 25
= 10
Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.
Model Problems
Multiplying a polynomial with a monomial
5 3 2 7( )3 2 5 7 5
Distributive Property
3 2 5 7 5 3 10 35
Rule #1
2 3 6 3( )( ) Multiplying polynomial with a polynomial
FOIL
2 6 2 3 6 3 3 3( ) 12 4 3 3( )
9 4 3
Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.
Model Problems
Simplify.3 32 44 3 16x x
3 32 44 3 16( ) x x
Multiply coefficients
Multiply radicands
3 2 412 16x x
3 612 16x3 612 8 2x Simplify
2 312 2 2x 2 324 2x
Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.
Model Problems
Simplify.3 4 332 2x x
3 4
3
32
2
x
x
3 4
3
1 32
2
x
x
3 3132
2x
3 318 4
2x 31
2 42
x 3 4x
4
31 32
2
x
x
Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.
Model Problems - Find the areas:
square
12
A = e2
A = 1212 1212
212144 units
parallelogram
22
20
A = bhA = 2220
2202 402
Simplify: 1042 1042 1022
104
Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.
Application Problem
A city park department rents paddle boats at docks near each entrance to the park. About how far is it to paddle from one dock to the other?
200 m
400 m
Pythagorean Theorem c2 = a2 + b2
Pythagorean Theorem c2 = a2 + b2
c2 = 4002 + 2002
c2 = 160,000 + 40,000c2 = 200,000c = 000,200
000,405 000,405
.52002005 ft .2.447 ft