How is $\sqrt{9+2\sqrt6+2\sqrt8+2\sqrt{12}}$ simplified into $\sqrt2+\sqrt3+\sqrt4$ ?
2026-04-12 09:31:45.1775986305
How to simplify root over root expressions?
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It's just the observation that $$(\sqrt2+\sqrt3+\sqrt4)^2=2+3+4+2\sqrt2\sqrt3+2\sqrt2\sqrt4+2\sqrt3\sqrt4=9+2\sqrt6+2\sqrt8+2\sqrt{12}.$$