Solving Cube Root of 26±15√3 - I am not sure how

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Discussion Overview

The discussion revolves around the mathematical problem of proving the identities involving the cube roots of expressions containing square roots, specifically \(\sqrt[3]{26+15\sqrt{3}}\) and \(\sqrt[3]{26-15\sqrt{3}}\). The scope includes mathematical reasoning and problem-solving techniques.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant requests proof for the identities involving the cube roots.
  • Another participant suggests that the problem is simple and asks what the original poster has tried.
  • A participant expresses uncertainty about how to approach the problem.
  • One participant proposes cubing both sides as a potential method to solve the problem.
  • A later reply indicates that the original poster has found the problem to be simple after considering the suggestion.

Areas of Agreement / Disagreement

There appears to be a lack of consensus on the difficulty of the problem, with some participants viewing it as simple while others express uncertainty about how to proceed.

Contextual Notes

Participants have not detailed their specific approaches or assumptions, and the discussion does not resolve the mathematical steps involved in the proof.

Jim Kata
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prove

[tex]\sqrt[3]{26+15\sqrt{3}} = 2 + \sqrt{3}[/tex]

and
[tex]\sqrt[3]{26-15\sqrt{3}} = 2 - \sqrt{3}[/tex]

I am not sure how to do this
 
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Uh, this is AWFULLY simple. What have you tried?
 
to be honest I have no idea what to do
 
Well since one side is a cube root, how about you try cubing both sides.
 
got it, yes extremely simple
 

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