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

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SUMMARY

The discussion focuses on proving the identities of the cube roots of the expressions \( \sqrt[3]{26+15\sqrt{3}} \) and \( \sqrt[3]{26-15\sqrt{3}} \). The identities are established as \( \sqrt[3]{26+15\sqrt{3}} = 2 + \sqrt{3} \) and \( \sqrt[3]{26-15\sqrt{3}} = 2 - \sqrt{3} \). The method suggested involves cubing both sides to simplify the expressions and verify the results. Participants confirm that the approach is straightforward once the cubing technique is applied.

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Jim Kata
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prove

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

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

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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