Operations with radicals

Operations with radicals

Lessons

\cdot even root: evenpositive=defined{^{even}}\sqrt{positive}=defined
i.e. 64=8\sqrt{64}=8
evennegative=undefined{^{even}}\sqrt{negative}=undefined
i.e. 64=undefined\sqrt{-64}=undefined

\cdot odd root: oddpositiveornegative=defined{^{odd}}\sqrt{positive\;or\;negative}=defined
i.e. 364=4{^3}\sqrt{64}=4
i.e. 364=4{^3}\sqrt{-64}=-4
  • 1.
    \cdotWhat is a “radical”?
    \cdotsquare root VS. cubic root
    \cdotcommom squares to memorize

  • 2.
    Evaluating Radicals Algebraically
    Without using a calculator, evaluate:
    a)
    9\sqrt { - 9}

    b)
    327{^3}\sqrt{{ - 27}}

    c)
    6164{^6}\sqrt{{\frac{1}{{64}}}}

    d)
    481{^4}\sqrt{{ - 81}}

    e)
    93649{^3}\sqrt{{64}}


  • 3.
    Evaluating Radicals Using a Calculator
    Use a calculator to determine:
    a)
    6729{\;}{^6}\sqrt{{729}}

    b)
    51024{^5}\sqrt{{-1024}}

    c)
    532243{^5}\sqrt{{\frac{{32}}{{243}}}}

    d)
    6600{^6}\sqrt{{600}}

    e)
    50.5{^5}\sqrt{{0.5}}

    f)
    34436\frac{3}{4}{^4}\sqrt{{36}}


  • 4.
    Radical Rules
    Combining radicals: Do's and Don'ts

  • 5.
    Determine whether the following statements are true or false.
    a)
    2×3=6\sqrt 2 \times \sqrt 3 = \sqrt 6

    b)
    2010=2\frac{{\sqrt {20} }}{{\sqrt {10} }} = \sqrt 2

    c)
    15302=900\sqrt {15} \cdot\sqrt {30} \cdot\sqrt 2 = 900

    d)
    35325=5{^3}\sqrt{5} \cdot {^3}\sqrt{{25}} = 5