Radical Chain (NMC (National Mathletics Challenge) 2026)

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Algebra · NMC (National Mathletics Challenge) 2026 | proposed by @2147483647 1000

Find the value of $(1+\sqrt{3})(1+\sqrt[4]{3})(1+\sqrt[8]{3})(1+\sqrt[16]{3})(1-\sqrt[16]{3})$.