Operations with radicals

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  1. \cdotWhat is a "radical"?
    \cdotsquare root VS. cubic root
    \cdotcommon squares to memorize
  1. Evaluating Radicals Algebraically
    Without using a calculator, evaluate:
    1. 9\sqrt { - 9}
    2. 327{^3}\sqrt{{ - 27}}
    3. 6164{^6}\sqrt{{\frac{1}{{64}}}}
    4. 481{^4}\sqrt{{ - 81}}
    5. 93649{^3}\sqrt{{64}}
  2. Evaluating Radicals Using a Calculator
    Use a calculator to determine:
    1.   6729{\;}{^6}\sqrt{{729}}
    2. 51024{^5}\sqrt{{-1024}}
    3. 532243{^5}\sqrt{{\frac{{32}}{{243}}}}
    4. 6600{^6}\sqrt{{600}}
    5. 50.5{^5}\sqrt{{0.5}}
    6. 34436\frac{3}{4}{^4}\sqrt{{36}}
  3. Radical Rules
    Combining radicals: Do's and Don'ts
    1. Determine whether the following statements are true or false.
      1. 2×3=6\sqrt 2 \times \sqrt 3 = \sqrt 6
      2. 2010=2\frac{{\sqrt {20} }}{{\sqrt {10} }} = \sqrt 2
      3. 15302=900\sqrt {15} \cdot\sqrt {30} \cdot\sqrt 2 = 900
      4. 35325=5{^3}\sqrt{5} \cdot {^3}\sqrt{{25}} = 5
    Topic Notes
    \cdot even root: evenpositive=defined{^{even}}\sqrt{positive}=defined
    i.e. 64=8\sqrt{64}=8
    i.e. 64=undefined\sqrt{-64}=undefined

    \cdot odd root: oddpositive  or  negative=defined{^{odd}}\sqrt{positive\;or\;negative}=defined
    i.e. 364=4{^3}\sqrt{64}=4
    i.e. 364=4{^3}\sqrt{-64}=-4