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Find-4-2-3-5-2-3-5-2-14-4-




Question Number 190024 by Shrinava last updated on 26/Mar/23
Find:  (√(4+(√2))) ∙ (√(3+(√(5+(√2))))) ∙ (√(3−(√(5+(√2))))) + ∣(√(14))−4∣
$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{4}+\sqrt{\mathrm{2}}}\:\centerdot\:\sqrt{\mathrm{3}+\sqrt{\mathrm{5}+\sqrt{\mathrm{2}}}}\:\centerdot\:\sqrt{\mathrm{3}−\sqrt{\mathrm{5}+\sqrt{\mathrm{2}}}}\:+\:\mid\sqrt{\mathrm{14}}−\mathrm{4}\mid \\ $$
Answered by SEKRET last updated on 26/Mar/23
 (√(4+(√2)  )) (√(3^2 −(5+(√2))))  + 4 − (√(14))     (√(4+(√2) )) (√(4−(√2) )) +4 − (√(14))     (√(4^2 −2)) +4 −(√(14))     (√(14 )) +4 − (√(14))    4  answer
$$\:\sqrt{\mathrm{4}+\sqrt{\mathrm{2}}\:\:}\:\sqrt{\mathrm{3}^{\mathrm{2}} −\left(\mathrm{5}+\sqrt{\mathrm{2}}\right)}\:\:+\:\mathrm{4}\:−\:\sqrt{\mathrm{14}} \\ $$$$\:\:\:\sqrt{\mathrm{4}+\sqrt{\mathrm{2}}\:}\:\sqrt{\mathrm{4}−\sqrt{\mathrm{2}}\:}\:+\mathrm{4}\:−\:\sqrt{\mathrm{14}}\: \\ $$$$\:\:\sqrt{\mathrm{4}^{\mathrm{2}} −\mathrm{2}}\:+\mathrm{4}\:−\sqrt{\mathrm{14}} \\ $$$$\:\:\:\sqrt{\mathrm{14}\:}\:+\mathrm{4}\:−\:\sqrt{\mathrm{14}} \\ $$$$\:\:\mathrm{4}\:\:\boldsymbol{\mathrm{answer}} \\ $$$$ \\ $$

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