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What syntax to display roots (like squareroot --> nth root)?

Posted 9 years ago

Hello, I teach in school and regularly provide links to wolframalpha with the calculation so that students know my results are correct. For this I want to have the input exactly as provided to the students.

In Latex I can write the n'th root of x as " \sqrt[n]{x}" unfortunately wolframalpha didn't recognize this command at all and takes the squareroot of n times x. (I am aware that \sqrt as command for a general root is misleading) For the life of me I can't find the right syntax to get the input of n'th root of x.

Please be aware that I know it's the same as x^(1/n) but I would like my students to see that root symbol with a little n over it. I hope you can help and perhaps upvote to implement this LaTeX notation in Wolframalpha as well. Kind regards Richard

POSTED BY: Rick K.
3 Replies
Posted 9 years ago

Richard,

Ah, that makes sense. So, if I now understand you correctly, you would like the input to WolframAlpha to be the same input you've already created in LaTeX, so that you don't have to maintain two versions to keep the classroom materials in sync with what students would see at WolframAlpha. That would certainly be desirable. As it turns out, I think this should actually work for you, and I don't understand why it isn't. Again, I put the expressions you listed into WolframAlpha, and they worked for me. Maybe the WolframAlpha output isn't exactly the same as your materials, but it should be close enough for students to not be confused. Or maybe there is a problem in how you're linking to WolframAlpha.

Do you actually have Mathematica in your school? Mathematica has good output for mathematical expressions, and it even has a TeXForm function, so you could sort of "go the other way". You could let Mathematica generate the TeX expression that you feed to whatever tool is formatting your materials. Or you could just do the whole thing in Mathematica.

Sorry I can't be of more help, but I'm just not seeing the problems with your example expressions in WolframAlpha, so I don't know what's going wrong.

POSTED BY: Eric Rimbey
Posted 9 years ago

(edit: I just tried it today with replacing it by adding ( ...)^{1/3} and it displays the root symbol, I could swear that it displayed to the power of 1/3 yesterday, sorry I seemed to be confused)

Hi Eric,

Thanks for the quick response. I tried \sqrt[3]{27} myself right now and it worked, I don't know why didn't try it before and still put it as an example.

However the following expressions do not work:

\sqrt[3]{v^2(v^6 * \sqrt{v^{-3}})^{\frac{2}{3}}}

or

\sqrt[3]{\frac{x^{-7}}{x^{-4}}}

Sorry for the cunfusion underneath, when I wrote "input", I meant what wolframalpha displays as "input" (root symbol and all). Thus on the exercise sheet of the students, I display the cubic root symbol, and not "to the power of 1/3".

On the PDF of the solution sheet they have a link to wolframalpha and if they click on it, I would like them to see the same thing as on their printed exercice sheet.

If they see for example \sqrt[3]{27} (processed through LaTeX to look like a root) on their exercice sheet and 27^{1/3} on wolframalpha, they might think it's a different exercise.

POSTED BY: Rick K.
Posted 9 years ago

Richard,

All of these work for me in WolframAlpha:

  • cube root of 5
  • 5^1/3
  • \sqrt[3]{5}
  • \sqrt[n]{x}
  • nth root of x

I'm not quite sure what to make of your statement "I want to have the input exactly as provided to the students". If the only input you allow is LaTeX, how do students use their calculators? Do you require them to write out syntactically correct LaTeX on tests? LaTeX is a presentation system. It is not a good notation for computation or symbolic manipulation. I'm sorry to sound critical, so maybe you can provide more context if none of the above input formats satisfies your need.

POSTED BY: Eric Rimbey
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