Cubed roots

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  1. jrowe's Avatar
    1 27-07-2012  13:28
    • New Member
    • Posts: 15
    Cubed roots
    Hi,
    I'm stuck on an equation. x^3=16000 * sqrt 2. This apparently can be reduced down to x = 20 * sqrt 2. I don't know how to do this, can anyone give me any help. Is it possible to cube root a square? I can find the answer 28.28 when using a calculator but would like to actually understand it. Many thanks.
  2. nuodai's Avatar
    2 27-07-2012  13:33
    • PS Helper
    • TSR Legend
    Re: Cubed roots
    (Original post by jrowe)
    Hi,
    I'm stuck on an equation. x^3=16000 * sqrt 2. This apparently can be reduced down to x = 20 * sqrt 2. I don't know how to do this, can anyone give me any help. Is it possible to cube root a square? I can find the answer 28.28 when using a calculator but would like to actually understand it. Many thanks.
    Your best bet is to convert it all to indices.

    First notice that 16 = 2^4 and 1000=10^3, so 16000 = 2^4 \times 10^3. And \sqrt{2} = 2^{\frac{1}{2}}, so by the laws of indices we have

    x^3 = 2^{\frac{9}{2}} \times 10^3

    Now take the cube root of both sides, using the laws of indices to simplify the RHS, and you'll see that it simplifies to give the above answer.
  3. notnek's Avatar
    3 27-07-2012  13:35
    • TSR Demigod
    • Location: Bangkok, Thailand
    Re: Cubed roots
    16000 \sqrt{2} = 8000 \times 2 \times \sqrt{2} = 8000 \times \sqrt{2}^3

    Can you do it now?
  4. jrowe's Avatar
    4 28-07-2012  00:24
    • New Member
    • Posts: 15
    Re: Cubed roots
    OK, so then
    X^3= 20^3 * sqrt2 ^3
    And then just get rid of all the ^3,
    If that's right then thank you!!!
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