7'3: Operations on radical expressions

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7.3 Operations on radical expressions

• Consider the following examples
• Sqrt(4) sqrt(25)
• 2 5 10
• But consider .
• Sqrt(4) sqrt(25) sqrt(425)
• sqrt(100) 10
• Sqrt(36)/sqrt(4) 6/2 3
• Sqrt(36/4) sqrt(9) 3

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Rules for Radical Expressions

• Let a and b be real numbers, where
  are both defined. Then
  

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Multiply
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Multiply
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Multiply
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Divide or simplifyLeave answers in radical form
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Divide or simplifyLeave answers in radical form
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Divide or simplifyLeave answers in radical form
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Divide or simplifyLeave answers in radical form
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Simplify
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Simplify
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Simplify
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Simplify
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Addition Subtraction of Radical Expressions

• Recall 2x2 5x2
• (25)x2 7x2
• 2x2 5x
• 2x2 5x
• Likewise 2?(3) 5?(3)
• (25)?(3) 7?(3)
• And 2?(3) 5?(2)
• 2 ?(3) 5 ?(2)
• Unless ..

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Finding Like Radicals

• Write each pair as like radicals if possible

• Factor each radicand using the largest perfect
  square possible as one of the factors

• Take the root of the perfect square

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Finding Like Radicals

• Write each pair as like radicals if possible

• Factor each radicand using the largest perfect
  square possible as one of the factors

• Take the root of the perfect square

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Finding Like Radicals

• Write each pair as like radicals if possible

• Factor each radicand using the largest perfect
  cube possible as one of the factors

• Take the root of the perfect cube mult. By the
  coefficient

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Simplify
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Add or Subtract
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Add or Subtract
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7.3 Homework

• 1-6 7-10 9-35 odds 17 - 24 53-56 63-64.