W A T K I N S - J O H N S O N C O M P A N Y Semiconductor Equipment Group

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Chabot Mathematics
7.1 Cube nth Roots
Bruce Mayer, PE Licensed Electrical Mechanical
EngineerBMayer_at_ChabotCollege.edu
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Review

• Any QUESTIONS About
• 7.1 ? Square-Roots and Radical Expessions
• Any QUESTIONS About HomeWork
• 7.1 ? HW-30

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Cube Root

• The CUBE root, c, of a Number a is written as

• The number c is the cube root of a, if the third
  power of c is a that is if c3 a, then

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Example ? Cube Root of No.s

• Find Cube Roots
• a) b) c)

• SOLUTION
• a)

As 0.20.20.2 0.008

• b)

As (-13)(-13)(-13) -2197
As 33 27 and 43 64,so (3/4)3 27/64

• c)

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Cube Root Functions

• Since EVERY Real Number has a Cube Root Define
  the Cube Root Function

• The GraphReveals
• Domain all Real numbers
• Range all Real numbers

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Evaluate Cube Root Functions

• Evaluate Cube Root Functions

• SOLUTION (using calculator)

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Simplify Cube Roots

• For any Real Number, a

• Use this property to simplify Cube Root
  Expressions.
• For EXAMPLE ? Simplify

• SOLUTION

because (3x)(3x)(3x) 27x3
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nth Roots

• nth root The number c is an nth root of a number
  a if cn a.
• The fourth root of a number a is the number c for
  which c4 a. We write for the nth root.
  The number n is called the index (plural,
  indices). When the index is 2 (for a Square
  Root), the Index is ommitted.

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Odd Even nth Roots ?

• When the index number, n, is ODD the root itself
  is also called ODD
• A Cube-Root (n 3) is Odd. Other Odd roots share
  the properties of Cube-Roots
• the most important property of ODD roots is that
  we can take the ODD-Root of any Real Number
  positive or NEGATIVE
• Domain of Odd Roots (-?, ?)
• Range of Odd Roots (-?, ?)

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Example ? nth Roots of No.s

• Find ODD Roots
• a) b) c)

• SOLUTION
• a)

Since 35 243

• b)

As (-3)(-3)(-3)(-3)(-3) -243
When the index equals the exponent under the
radical we recover the Base

• c)

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Odd Even nth Roots ?

• When the index number, n, is EVEN the root itself
  is also called EVEN
• A Sq-Root (n 2) is Even. Other Even roots share
  the properties of Sq-Roots
• The most important property of EVEN roots is that
  we canNOT take the EVEN-Root of a NEGATIVE
  number.
• Domain of Even Roots xx 0
• Range of Even Roots yy 0

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Example ? nth Roots of No.s

• Find EVEN Roots
• a) b) c)

• SOLUTION
• a)

Since 34 81

• b)

Even Root is Not a Real No.
Use absolute-value notation since m could
represent a negative number

• c)

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Simplifying nth Roots
n a
Even Positive Positive a
Negative Not a real number a
Odd Positive Positive a
Negative Negative a
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Example ? Radical Expressions

• Find nth Roots
• a) b) c)

• SOLUTION
• a)

• b)

• c)

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WhiteBoard Work

• Problems From 7.1 Exercise Set
• 50, 74, 84, 88, 98, 102

• Principalnth Root

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All Done for Today
SkidMarkAnalysis
Skid Distances
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Chabot Mathematics
Appendix
Bruce Mayer, PE Licensed Electrical Mechanical
EngineerBMayer_at_ChabotCollege.edu

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Graph y x

• Make T-table

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