Download 11.1 Simplifying Radicals

11.1 Simplifying Radical Expressions
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2
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Definitions
Simplifying Radicals
Practice Problems
Definitions
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Perfect Squares
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4 4 2
64  64  8
9 9 3
81  81  9
16  16  4
100  100  10
25  25  5
121  121  11
36  36  6
144  144  12
49  49  7
169  169  13
How a Square Root Works
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2
42
Simplifying Square Roots
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
Steps
 Factor
the radicand into the product of the largest
factor that is a perfect square
 Separate the square root into 2 separate square roots
 Solve the perfect square
 Check to make sure you can’t factor the radicand by
another perfect square
Simplifying a Square Root Example
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12
90
43
9 10
4 3
9  10
2 3
3 10
Multiplying Square Roots
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
Steps
 Multiply
the real numbers & leave outside the square
root
 Multiply the radicands to each other & leave inside the
square root
 Simplify the square root if possible
Multiplying a Square Root Example
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3  15
95
315
9 5
45
3 5
Multiplying a Square Root Example
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4 32 6
8 9 2
4  2 3 6
83 2
8 18
24 2
8 92
Simplifying a Square Root with
Variables
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
Steps
 Rewrite
the variable as a square using the exponent
rules
 Squares (2nd power) will cancel with square roots
Square Root Variable Example
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y
12
x
6 2
(x )
3
y y
2
y  y
2
x
6
y y
Putting It All Together
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4
5 3
40 x y z
40  x  y  z
4
5
3
4 10  ( x )  y  y  z  z
2
2
4
2
4  10  ( x )  ( y )  y  z  z
2
2
2 2
2
Putting It All Together (Cont.)
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4  10  ( x )  ( y )  y  z  z
2
2
2 2
2 10  x  y  y  z  z
2
2
2
2
2 x y z 10 yz
2
Practice Problems
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
Page 589-590
Problems 4-8, 14-25
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