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Question Number 194389 by mathlove last updated on 05/Jul/23

$$\sqrt{\sqrt{49+20\sqrt{6}}}=?$$

Answered by som(math1967) last updated on 05/Jul/23

$$\sqrt{\sqrt{5^2+{\left(2\sqrt{6}\right)}^2+2.5.2\sqrt{6}}}$$$$\sqrt{\sqrt{{(5+2\sqrt{6})}^2}}$$$$=\sqrt{5+2\sqrt{6}}$$$$=\sqrt{{(\sqrt{3}+\sqrt{2})}^2}=\sqrt{3}+\sqrt{2}$$

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