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Question Number 139468 by mathdanisur last updated on 27/Apr/21

prove:  (√(3+(√2)−(√(9+4(√2))))) = (√(2−(√2)))

$${prove}:\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{9}+\mathrm{4}\sqrt{\mathrm{2}}}}\:=\:\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$

Answered by OlafThorendsen last updated on 27/Apr/21

x =  (√(3+(√2)−(√(9+4(√2)))))  x =  (√(3+(√2)−(√((1+2(√2))^2 ))))  x =  (√(3+(√2)−(1+2(√2))))  x =  (√(2−(√2)))

$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{9}+\mathrm{4}\sqrt{\mathrm{2}}}} \\ $$$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} }} \\ $$$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right)} \\ $$$${x}\:=\:\:\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$

Commented by mathdanisur last updated on 02/May/21

thanks sir

$${thanks}\:{sir} \\ $$

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