How to simplify $\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}$ The answer is 2. But I want to learn how to simplify this expression without the use of calculator.

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*$7-5\sqrt 2 = 1-3\sqrt{2} + 6 - 2 \sqrt{2} = 1^3+\dbinom{3}{1}(-\sqrt{2})+\dbinom{3}{2}*(-\sqrt{2})^2+(-\sqrt{2})^3=(1-\sqrt{2})^3$ (By binomial theorem:https://en.wikipedia.org/wiki/Binomial_theorem)

*$7+5\sqrt 2 = 1+3\sqrt{2} + 6 + 2 \sqrt{2} = (1+\sqrt{2})^3$

