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Neat Number Trick

  1. Nov 17, 2006 #1
    Hey all

    Just thought I would share something I observed:

    [tex] 2 \sqrt[3]{8} = \sqrt[3]{64}[/tex]


    Or [tex] 2 \sqrt[5]{10} = \sqrt[5]{320} [/tex]

    [tex] 2^{5} \times 10 = 320 \rightarrow \sqrt[5]{320} [/tex]

    You raise the number outside to the power, and then multiply by the inside number.

    Has this already been known?
     
    Last edited: Nov 17, 2006
  2. jcsd
  3. Nov 17, 2006 #2

    chroot

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    Yes, it's a pretty basic consequence of the way that exponents work.

    [itex]
    2 \cdot \left( 8 \right)^{1/3} = \left( {2^3 } \right)^{1/3} \cdot \left( 8 \right)^{1/3} = \left( {2^3 \cdot 8} \right)^{1/3} = \left( {64} \right)^{1/3}
    [/itex]

    - Warren
     
  4. Nov 17, 2006 #3
    wow I am an idiot. Thanks for pointing that out.
     
  5. Nov 17, 2006 #4

    chroot

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    You're not an idiot at all. In fact, it'd be wonderful if every student was motivated to sit down and just explore math the way you just did. They'd learn so much more.

    - Warren
     
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