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I thought up a new approach to the problem about \(\large \sqrt[3]{\sqrt[3]{2} - 1} \) and its simplifications​. I know Calvin posted this a while back and I was wondering if any of you had a link so I can answer it.

Note by Sal Gard
5 months ago

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Thanks. Sorry for inconvenience. Sal Gard · 5 months ago

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@Sal Gard Why apologize? You did nothing wrong? We're here to learn.... Pi Han Goh · 5 months ago

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Thanks for the solution. I already had this but I was looking for the problem, not the answer. Thanks anyway. Sal Gard · 5 months ago

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@Sal Gard ARML 1997 Pi Han Goh · 5 months ago

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Rationalize numerator by multiplying the expression by \( \dfrac{\sqrt[3]{\sqrt[3]{4} + \sqrt[3]{2} + 1}}{\sqrt[3]{\sqrt[3]{4} + \sqrt[3]{2} + 1}} \) then simplify the expression, then multiply it by \( \dfrac{\sqrt[3]{3}}{\sqrt[3]{3}} \), you get \( \dfrac{ \sqrt[3]{3}}{1 + \sqrt[3]{3}} \). Finally, rationalize the denominator to obtain \( \sqrt[3]{\dfrac49} + \sqrt[3]{-\dfrac29} + \sqrt[3]{\dfrac19} \). Pi Han Goh · 5 months ago

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