I'd like to ask how to denest the nested radical $\sqrt{5^{\frac{1}{3}}-4^{\frac{1}{3}}}$?
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what makes you think it can be denested? – farruhota Aug 21 '19 at 06:29
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It seems that Ramanujan has got the answer $\frac{1}{3}(-25^\frac{1}{3}+20^\frac{1}{3}+2^\frac{1}{3})$. My following question is how to check whether $\sqrt{p^\frac{1}{3}-q^\frac{1}{3}}$ could be denested. – Hang Wu Aug 21 '19 at 06:33
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1see this post: https://math.stackexchange.com/questions/194030/simplify-sqrt-sqrt35-sqrt34?noredirect=1&lq=1 – farruhota Aug 21 '19 at 07:03
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1@Hang Wu, see this post for a general identity for such radicals. – Mourad Jan 28 '20 at 10:26
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Great answer. Thanks for your link. – Hang Wu Jan 29 '20 at 04:43