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Bookworm14

  • one year ago

Help with some simple exponents. Can you show me how to handowork 2^1.5 ?

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  1. Bookworm14
    • one year ago
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    I know the answer by using a calculator, but I have to show how to handwork it.

  2. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} &= 2\times \sqrt{2} \hspace{.33em}\\~\\ \end{align}}\)

  3. triciaal
    • one year ago
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    1.5 = 3/2

  4. triciaal
    • one year ago
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    |dw:1440432575903:dw|

  5. Bookworm14
    • one year ago
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    This is great! Thank you!

  6. triciaal
    • one year ago
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    welcome

  7. SolomonZelman
    • one year ago
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    We can find \(\sqrt{2}\) (or other roots) by hand, if you are familiar with differentiation.

  8. SolomonZelman
    • one year ago
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    \(\sqrt{x}~(near~x=2)~=f(1)+f'(1)(x-1)=\sqrt{1}+\frac{1}{2\sqrt{1}}(x-1)=1+\frac{1}{2}(x-1)\) \(\sqrt{2}\approx 1+\frac{1}{2}(2-1)=1.5\)

  9. SolomonZelman
    • one year ago
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    or perhaps this sounds like a metal retarded-ness right now....

  10. SolomonZelman
    • one year ago
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    well, just go by \(\sqrt[C]{A^{B}}=A^{B/C}\)

  11. Bookworm14
    • one year ago
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    @SolomonZelman I keep working it out but when I substitute I keep getting \[2\sqrt(2^3)\] but that doesn't equal 2.828 ?

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