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Question Number 83370 by Power last updated on 01/Mar/20

Commented by Power last updated on 01/Mar/20

$$\mathrm{solve}\mathrm{pls}$$

Commented by mr W last updated on 01/Mar/20

$$=\sqrt{2+\sqrt{3}}\times \sqrt{2+\sqrt{2+\sqrt{3}}}\times \left(\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\times \sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\right)$$$$=\sqrt{2+\sqrt{3}}\times \sqrt{2+\sqrt{2+\sqrt{3}}}\times \left(\sqrt{2^2-{\left(\sqrt{2+\sqrt{2+\sqrt{3}}}\right)}^2}\right)$$$$=\sqrt{2+\sqrt{3}}\times \sqrt{2+\sqrt{2+\sqrt{3}}}\times \left(\sqrt{4-2-\sqrt{2+\sqrt{3}}}\right)$$$$=\sqrt{2+\sqrt{3}}\times \left(\sqrt{2+\sqrt{2+\sqrt{3}}}\times \sqrt{2-\sqrt{2+\sqrt{3}}}\right)$$$$=\sqrt{2+\sqrt{3}}\times \left(\sqrt{2^2-{\left(\sqrt{2+\sqrt{3}}\right)}^2}\right)$$$$=\sqrt{2+\sqrt{3}}\times \left(\sqrt{4-2-\sqrt{3}}\right)$$$$=\sqrt{2+\sqrt{3}}\times \sqrt{2-\sqrt{3}}$$$$=\sqrt{2^2-{\left(\sqrt{3}\right)}^2}$$$$=\sqrt{4-3}$$$$=1$$

Commented by Power last updated on 02/Mar/20

$$\mathrm{thank}\mathrm{you}$$

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