7-1 roots and radical expressions · 71 roots and radical expressions 10 february 05, 2010 jan...
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71 Roots and Radical Expressions
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February 05, 2010
Jan 211:37 PM
71 Roots and Radical Expressions
Objective:Simplify nth roots.
71 Roots and Radical Expressions
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February 05, 2010
Jan 211:40 PM
Check Skills You'll Need
Write each number as a square of a number.
1. 25 2. 0.09 3. 4/49
Write each expression as a square of an expression.
4. x10 5. x4y2 6. 169x6y12
71 Roots and Radical Expressions
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February 05, 2010
Nov 37:32 AM
List the squares of all the numbers 1‐15.
71 Roots and Radical Expressions
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Nov 37:32 AM
List the cubes of all the numbers 1‐10.
71 Roots and Radical Expressions
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Nov 37:32 AM
List the cube roots of all the numbers 1‐1000.
1
1000
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February 05, 2010
Jan 211:50 PM
Look at the following pattern:
Since 52 = 25, 5 is a square root of 25.Since 53 = 125, 5 is a cube root of 125.Since 54 = 625, 5 is a fourth root of 625.Since 55 = 3125, 5 is a fifth root of 3125.
This pattern leads to the definition of nth root.
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February 05, 2010
Jan 211:57 PM
Since 24 = 16 and (‐2)4 = 16, both 2 and ‐2 are fourth roots of 16.
Since there is no real number x such that x4 = ‐16, ‐16 has no real fourth root.
Since ‐5 is the only real number whose cube is ‐125, ‐5 is the only real cube root of ‐125.
71 Roots and Radical Expressions
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February 05, 2010
Jan 212:23 PM
Find all the real cube roots.
a. 0.008 b. ‐1000 c. 1/27
(0.2)3= 0.008 (‐10)3 = ‐1000 (1/3)3 = 1/27
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February 05, 2010
Jan 212:29 PM
Find all the real fifth roots.
d. 0 e. ‐1 f. 32
0 ‐1 2
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February 05, 2010
Jan 212:32 PM
A radical sign is used to indicate a root.
The index gives the degree of the root.
The number under the radical sign is the radicand.
When a number has TWO real roots, the POSITIVE root is called the PRINCIPAL ROOT.
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Jan 231:34 PM
When a number has TWO real roots, the POSITIVE root is called the PRINCIPAL ROOT.
The PRINCIPAL fourth root of 16 is 2
because equals . The other
fourth root of 16 is written as ,
which equals 2.
∜16 ∜24
∜16
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February 05, 2010
Jan 231:58 PM
Find each real number root.
a. ∛-8 b. √-100 c. ∜81
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February 05, 2010
Jan 232:10 PM
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February 05, 2010
Jan 232:19 PM
Simplify each radical expression.
a. √4x6 b. ∛a3b6 c. ∜x4y8
√22(x3)2 ∛a3(b2)3 ∜x4(y2)4
√(2x3)2 ∛(ab2)3 ∜(xy2)4
2|x3| ab2 |x|y2
Absolute value symbols must not be used here. If a is negative, then the radicand is negative and the root must also be
negative.
Absolute value symbols ensure that the root is
positive when x is negative. They are not needed
for y because y2 is never negative.
Absolute value symbols ensure that the root is
positive when x is negative.
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February 05, 2010
Feb 58:30 AM
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Jan 248:30 AM
HOMEWORK
p. 372 #1 28, 39 54