pouvez vous m'aider s.v.pMerci d'avance..... Pergunta de ideia deichraqrm

June 2021 1 87 Report

pouvez vous m'aider s.v.p
Merci d'avance.

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eleanort

Réponse :

$A = \sqrt{5+\sqrt{11+\sqrt{25} } } \\A = \sqrt{5+\sqrt{11+5} } \\A = \sqrt{5\sqrt{16} } \\A = \sqrt{5+4} \\A = \sqrt{9} \\A = 3$

$B = \sqrt{6\sqrt{6\sqrt{6^{2} } } } \\B = \sqrt{6\sqrt{6*6} }\\B = \sqrt{6\sqrt{36} } \\B = \sqrt{6*6} \\B = \sqrt{36} \\B = 6$

$C = \sqrt{a^{2}+2ab+b^{2} } +\sqrt{a^{2}-2ab+b^{2} } \\C = \sqrt{(a+b)^{2} } + \sqrt{(a-b)^{2} } \\C = (a+b)(a-b)\\C = a^{2}-b^{2}$

$D = 7\sqrt{18} - \sqrt{98} - 2\sqrt{72} \\D = 7\sqrt{9*2}-\sqrt{49*2} - 2\sqrt{4*2*9} \\D = 7*3\sqrt{2} - 7\sqrt{2} - 2*2*3\sqrt{2} \\D = 21\sqrt{2} - 7\sqrt{2} - 12 \sqrt{2} \\D = 14\sqrt{2} - 12\sqrt{2} \\D = 2\sqrt{2}$

$E = \sqrt{27} - \sqrt{75} + \sqrt{108} \\E = \sqrt{9*3} - \sqrt{25*3} + \sqrt{4*3*9} \\E = 3\sqrt{3} - 5\sqrt{3} +2*3\sqrt{3} \\E = 3\sqrt{3} - 5\sqrt{3} + 6\sqrt{3}\\E = -2\sqrt{3} +6\sqrt{3} \\E = 4\sqrt{3}$