Radicals and Radical Expressions
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Transcript Radicals and Radical Expressions
Factor and Solve (5 minutes)
2
2
16 x 9 0
x 6x 9 0
( x 3)( x 3)
x3 x3
12 x x 1 0
2
(4 x 1)(3 x 1)
1
1
x
x
4
3
(4 x 3)(4 x 3)
3
3
x
x
4
4
18 x 12 x 0
2
6 x(3 x 2)
2
x0 x
3
Simplifying Radicals and
Complex Numbers
Objectives
• I can simplify Radicals to Lowest Terms
• I can simplify negative radicals using “i”
• I can simplify complex numbers using
– Addition
– Subtraction
– Multiplication
Symbols
• Radical symbol
Radical
Index#
Radicand
Radical Basics
• If there is no index number listed, it is
assumed to be a 2 (Square Root)
• The index number determines what root we
are looking for
Method for Simplifying
• Prime Factor the number under the house
(radical)
• Look at the value of the index number
• Cross off the index number of numbers or
variables to bring one out of the house.
• If you don’t have enough, then they stay
under the house.
Example 1
• Simplify:
36
2 2 33
2 2 33
23
6
• Factor the 36
36
2 18
2 9
3 3
Example 2
• Simplify:
12
• Factor the 12
12
2 23
2 23
2 3
2
6
2
3
Example 3
32
4 2
Example 3
20
2 5
Complex Numbers
Real Numbers
Rational
Irrational
Imaginary Numbers
Complex Numbers
The set of all numbers that can be written
in the format: a + bi ;
“a” is the real number part
“bi’ is the imaginary part
The Imaginary Unit
i 1 where i 1
2
Example 4
20
2 5i
Example 5
9
3i
Example 6
48
4 3i
Remember!
i 1
2
Simplifying Complex Numbers
• You can ONLY combine LIKE terms
– Real parts
– Imaginary parts
a bi
Real
Imaginary
(3 5i ) (7 8i)
10 3i
10 3i
(4 7i) (1 4i)
5 11i
5 11i
(6 2i ) (9 3i)
3 5i
3 5i
(8 7i ) (4 5i)
4 12i
4 12i
3(5 7i)
15 21i
15 21i
4(9 6i )
36 24i
36 24i
(3 4i)(9 2i)
27 6i 36i 8i
35 30i
2
i 1
2
(4 3i)(4 3i)
16 12i 12i 9i
25
2
i 1
2
Homework
• WS 5-2
• Quiz next class