Operations with radicals

Lessons

• Introduction
  $\cdot$What is a “radical”?
  $\cdot$square root VS. cubic root
  $\cdot$commom squares to memorize
  

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• 1.
  Evaluating Radicals Algebraically
  Without using a calculator, evaluate:
  a)

  $\sqrt { - 9}$
  
  
  b)

  ${^3}\sqrt{{ - 27}}$
  
  
  c)

  ${^6}\sqrt{{\frac{1}{{64}}}}$
  
  
  d)

  ${^4}\sqrt{{ - 81}}$
  
  
  e)

  $9{^3}\sqrt{{64}}$
  
  

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• 2.
  Evaluating Radicals Using a Calculator
  Use a calculator to determine:
  a)

  ${\;}{^6}\sqrt{{729}}$
  
  
  b)

  ${^5}\sqrt{{-1024}}$
  
  
  c)

  ${^5}\sqrt{{\frac{{32}}{{243}}}}$
  
  
  d)

  ${^6}\sqrt{{600}}$
  
  
  e)

  ${^5}\sqrt{{0.5}}$
  
  
  f)

  $\frac{3}{4}{^4}\sqrt{{36}}$
  
  

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• 3.
  Radical Rules
  Combining radicals: Do's and Don'ts

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• 4.
  Determine whether the following statements are true or false.
  a)

  $\sqrt 2 \times \sqrt 3 = \sqrt 6$
  
  
  b)

  $\frac{{\sqrt {20} }}{{\sqrt {10} }} = \sqrt 2$
  
  
  c)

  $\sqrt {15} \cdot\sqrt {30} \cdot\sqrt 2 = 900$
  
  
  d)

  ${^3}\sqrt{5} \cdot {^3}\sqrt{{25}} = 5$
  
  

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