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Is it possible knownto know if $4-\sqrt{2}-\sqrt[3]{3}-\sqrt[5]{5} \gt 0$ without useusing decimal numbers?

Is it possible known if $4-\sqrt{2}-\sqrt[3]{3}-\sqrt[5]{5} \gt 0$ without use decimal numbers?

Is it possible to know if $4-\sqrt{2}-\sqrt[3]{3}-\sqrt[5]{5} \gt 0$ without using decimal numbers?

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Prove $5$4-\sqrt{2}-\sqrt[3]{3}-\sqrt[5]{5} \gt 0$

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