Bookworm14
  • Bookworm14
Help with some simple exponents. Can you show me how to handowork 2^1.5 ?
Mathematics
schrodinger
  • schrodinger
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Bookworm14
  • Bookworm14
I know the answer by using a calculator, but I have to show how to handwork it.
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} &= 2\times \sqrt{2} \hspace{.33em}\\~\\ \end{align}}\)
triciaal
  • triciaal
1.5 = 3/2

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triciaal
  • triciaal
|dw:1440432575903:dw|
Bookworm14
  • Bookworm14
This is great! Thank you!
triciaal
  • triciaal
welcome
SolomonZelman
  • SolomonZelman
We can find \(\sqrt{2}\) (or other roots) by hand, if you are familiar with differentiation.
SolomonZelman
  • SolomonZelman
\(\sqrt{x}~(near~x=2)~=f(1)+f'(1)(x-1)=\sqrt{1}+\frac{1}{2\sqrt{1}}(x-1)=1+\frac{1}{2}(x-1)\) \(\sqrt{2}\approx 1+\frac{1}{2}(2-1)=1.5\)
SolomonZelman
  • SolomonZelman
or perhaps this sounds like a metal retarded-ness right now....
SolomonZelman
  • SolomonZelman
well, just go by \(\sqrt[C]{A^{B}}=A^{B/C}\)
Bookworm14
  • Bookworm14
@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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