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Question Number 123996 by mlj5 last updated on 29/Nov/20

(√((2^(14) +16^4 )/(2^(16) +2^(22) ))) calcule svp

$$\sqrt{\frac{\mathrm{2}^{\mathrm{14}} +\mathrm{16}^{\mathrm{4}} }{\mathrm{2}^{\mathrm{16}} +\mathrm{2}^{\mathrm{22}} }}\:{calcule}\:{svp} \\ $$

Answered by john_santu last updated on 30/Nov/20

(√((2^(14) +2^(16) )/(2^(16) +2^(22) ))) = (√((2^(14) (1+2^2 ))/(2^(14) (2^2 +2^8 ))))   =(√(5/(4+256)))= (√(5/(260)))  ≈ 0.138675  (√(5/(260)))  0.138675

$$\sqrt{\frac{\mathrm{2}^{\mathrm{14}} +\mathrm{2}^{\mathrm{16}} }{\mathrm{2}^{\mathrm{16}} +\mathrm{2}^{\mathrm{22}} }}\:=\:\sqrt{\frac{\mathrm{2}^{\mathrm{14}} \left(\mathrm{1}+\mathrm{2}^{\mathrm{2}} \right)}{\mathrm{2}^{\mathrm{14}} \left(\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{8}} \right)}} \\ $$$$\:=\sqrt{\frac{\mathrm{5}}{\mathrm{4}+\mathrm{256}}}=\:\sqrt{\frac{\mathrm{5}}{\mathrm{260}}}\:\:\approx\:\mathrm{0}.\mathrm{138675} \\ $$$$\sqrt{\frac{\mathrm{5}}{\mathrm{260}}} \\ $$$$\mathrm{0}.\mathrm{138675} \\ $$

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