$\sqrt{1+{\sqrt{4+\sqrt{{21}+{\sqrt{16}}}}}}=$

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Answer:

$\sqrt{1+{\sqrt{4+\sqrt{{21}+{\sqrt{16}}}}}}$

$=\sqrt{1+{\sqrt{4+\sqrt{21+4}}}}$

$=\sqrt{1+{\sqrt{4+5}}}=\sqrt{1+{\sqrt{9}}}=\sqrt4=2$

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