Transcript Chapter 7.1 Roots & Radical Expressions

Chapter 7.1
Roots & Radical Expressions
Definitions/Key Concepts
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25
square
52 _______,
5 is a ________
root of 25
125
cube
53 _______,
5 is a ________
root of 125
625
fourth
54 _______,
5 is a ________
root of 625
Definition of nth root for REAL NUMBERS:
an = b means a is the nth root of b
Summary of Possible Real Roots
Type of
Number
# of REAL nth roots,
when n is even
# of REAL nth roots,
when n is odd
Positive
2
1
0
1
1
Negative
0
1
EXAMPLE: Find All Real Roots
3
D) The cube root of -8/27 = _______
-2/3
A) The cube root of 27 = _______
+3
+ 2/3
E) The fourth root of 16/81 = _______
B) The fourth root of 81 = _______
No real roots F) The cube root of 0.008 = ________
0.2
C) The sixth root of -64 = ________
Radical Signs!
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You can use a radical sign to indicate the root.
The Index gives the degree of the root.
The radicand is the number under the radical sign.
Steps To Finding Real Roots
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Step 1: Deal with the NUMBERS first (if any). Use calculator as
necessary.
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Step 2: With Variables Inside the Radicand: You can just divide
the exponent by the INDEX. The whole number comes out of
the radical, and the remainder (if any) stays inside the radical.
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Step 2: Simplify the Expression
Example:
9x10
IMPORTANT NOTE: ONLY USE ABSOLUTE VALUE SYMBOLS
WHEN THE INDEX IS EVEN AND THE SIMPLIFIED EXPRESSION
CONTAINS A VARIABLE WITH AN ODD DEGREE
Additional Examples
3
a3b3
5
32x20y17
4 x16 y 4