## Bookworm14 one year ago Help with some simple exponents. Can you show me how to handowork 2^1.5 ?

1. Bookworm14

I know the answer by using a calculator, but I have to show how to handwork it.

2. mathmath333

\large \color{black}{\begin{align} &= 2\times \sqrt{2} \hspace{.33em}\\~\\ \end{align}}

3. triciaal

1.5 = 3/2

4. triciaal

|dw:1440432575903:dw|

5. Bookworm14

This is great! Thank you!

6. triciaal

welcome

7. SolomonZelman

We can find $$\sqrt{2}$$ (or other roots) by hand, if you are familiar with differentiation.

8. SolomonZelman

$$\sqrt{x}~(near~x=2)~=f(1)+f'(1)(x-1)=\sqrt{1}+\frac{1}{2\sqrt{1}}(x-1)=1+\frac{1}{2}(x-1)$$ $$\sqrt{2}\approx 1+\frac{1}{2}(2-1)=1.5$$

9. SolomonZelman

or perhaps this sounds like a metal retarded-ness right now....

10. SolomonZelman

well, just go by $$\sqrt[C]{A^{B}}=A^{B/C}$$

11. 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 ?