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$$\sqrt{\sqrt[3]{343} + 3 \times \sqrt{289} - \sqrt[3]{729}} =$$
We have $$\sqrt[3]{343} = 7$$, $$\sqrt{289} = 17$$ and $$\sqrt[3]{729} = 9$$. So the value is $$\sqrt{7 + 51 - 9} = \sqrt{49} = 7$$.
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