Download Section 8.3 Simplifying Radical Expressions

11/26/2012
Section 8.3
Simplifying Radical Expressions
Product Rule for Radicals
If n a and n b are real numbers and n is a natural number, then
n
a • n b = n ab.
You can use the product rule only when the radicals have the same index.
Multiply
10 •
3=
23 • t =
3
9 •
9x
3
44y =
1
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8•
5
6
12 =
Quotient Rule for Radicals
If
n
n
a and
n
a
=
b
n
n
b are real numbers and n is a natural number, then
a
b
Simplify each radical.
p y
16
=
49
13
=
49
w10
=
36
-
3
-
4
t
=
125
625
=
y4
2
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Express each radical in simplified form.
18 =
72 =
- 48 =
- 24 =
- 150 =
3
3
5
24 =
- 250 =
128 =
3
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Express each radical in simplified form. Assume all variables represent positive real numbers.
18m 2 =
3
32
=
216
256z12
− 3 64 y18
− 3 −216y15 x 6 z3
4
81 12 8
t u
256
4
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300z 3
23k 9 p14
3
64a15 b12
- 4 32k 5 m10
3
y17
125
5
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Simplify each radical.
4
502
6
8
Use the distance formula.
Distance Formula
The distance between points (x1, y1) and (x2, y2) is
d = ( x2 − x1 ) 2 + ( y2 − y1 ) 2
Slide 8.3- 12
6
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CLASSROOM
EXAMPLE 9
Using the Distance Formula
Find the distance between each pair of points. (2, –1) and (5, 3)
Solution:
Designate which points are (x1, y1) and (x2, y2).
(x1, y1) = (2, –1) and (x2, y2) = (5, 3) d = ( x2 − x1 ) 2 + ( y2 − y1 ) 2
d = (5 − 2) 2 + (3 − (−1)) 2
Start with the xvalue and y-value
of the same point.
d = (3) 2 + (4) 2
d = 9 + 16
d = 25 = 5
Slide 8.3- 13
CLASSROOM
EXAMPLE 9
Using the Distance Formula (cont’d)
Find the distance between each pairs of points. (–3, 2) and (0, −4)
Solution:
Designate which points are (x1, y1) and (x2, y2).
(x1, y1) = (–3, 2) and (x2, y2) = (0, −4) d = ( x2 − x1 ) 2 + ( y2 − y2 ) 2
d = (0 − ( −3)) 2 + ( −4 − 2) 2
d = (3) 2 + (−6) 2
d = 9 + 36
d = 45 = 3 5
Slide 8.3- 14
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Find the distance between the pair of points.
(8, 13) and (2, 5)
8