How to solve this equation?

Questions
1

Hey, I got that little equation:
\sqrt{(\frac{447,15\cdot 10^{-9} \cdot 0,87}{0,21 \cdot \sqrt{(0,87)^2 +(0,21)^2}})^2 \cdot (0,02)^2 +( \frac{447,15\cdot 10^{-9}}{\sqrt{(0,87)^2+(0,21)^2}}-\frac{447,15\cdot 10^{-9} \cdot \sqrt{(0,87)^2+(0,21)^2}}{(0,21)^2})^2\cdot(0,01)^2}
I tried several ways to solve this (means it should spit out a simple number) Suggestions?

2

Hi Ness,

\sqrt{(\frac{447,15\cdot 10^{-9} \cdot 0,87}{0,21 \cdot \sqrt{(0,87)^2 +(0,21)^2}})^2 \cdot (0,02)^2 +( \frac{447,15\cdot 10^{-9}}{\sqrt{(0,87)^2+(0,21)^2}}-\frac{447,15\cdot 10^{-9} \cdot \sqrt{(0,87)^2+(0,21)^2}}{(0,21)^2})^2\cdot(0,01)^2}

does not look like an equation. Please post the code that you used to try and evaluate that expression.

3

Replace decimal commas with decimal points, single backslashes with double backslashes, and \cdot with just a space:

ToExpression["\\sqrt{(\\frac{447.15  10^{-9}  0.87}{0.21 \
\\sqrt{(0.87)^2+(0.21)^2}})^2  (0.02)^2+( \\frac{447.15  \
10^{-9}}{\\sqrt{(0.87)^2+(0.21)^2}}-\\frac{447.15  10^{-9} \
\\sqrt{(0.87)^2+(0.21)^2}}{(0.21)^2})^2 (0.01)^2}", TeXForm, Hold]
ReleaseHold[%]

Check carefully the hold expression. You may need to insert extra braces {} in the input to get the correct interpretation.

4

let’s say g = … now solvable?

5

I mean I managed to transform my “equation” to Wolfram-code and set: solve g= Sqrt[({447, (15 0)/10^9, 87}/{0, 21 Sqrt[{0, 87}^2 + {0, 21}^2]})^2 {0, 2}^2 + ({447, 15/10^9}/Sqrt[{0, 87}^2 + {0, 21}^2] - {447, (15 Sqrt[{0, 87}^2 + {0, 21}^2])/10^9}/{0, 21}^2)^2 {0, 1}^2]. Now it’s just computing and computing

6

As Gianluca pointed out, that is not valid Wolfram code, decimal commas need to be replaced with decimal points etc. Check his answer, it gives the following

\sqrt{0.01^2 \left(\frac{1}{447.151^9 \sqrt{0.87^2+0.21^2}}-\frac{\sqrt{0.87^2+0.21^2}}{447.151^9 0.21^2}\right)^2+0.02^2 \left(\frac{0.87}{447.151^9 \left(0.21 \sqrt{0.87^2+0.21^2}\right)}\right)^2}

and corresponding WL code

Sqrt[(0.87/(447.151^9*(0.21*Sqrt[0.87^2 + 0.21^2])))^2*0.02^2 + 
   (1/(447.151^9*Sqrt[0.87^2 + 0.21^2]) - Sqrt[0.87^2 + 0.21^2]/(447.151^9*0.21^2))^2*0.01^2]

If that looks right then evaluate it. The result is

2.9798*10^-25