Question

Numărul -3√3 aparține intervalului: a) [-4√2,-5] b) (-√27,-1) c) [-4,-√3] d) [-5√3,-5√2] ​

Answer 1

introducem numărul sub radical:

$-3\sqrt{3} = -\sqrt{27}$

intervalele sunt:

$\Big[-4\sqrt{2};-5\Big] = \Big[-\sqrt{32};-\sqrt{25}\Big]$

$\Big(-\sqrt{27};-1\Big) = \Big(-\sqrt{27};-\sqrt{1}\Big)$

$\Big[-4;-\sqrt{3}\Big] = \Big[-\sqrt{16};-\sqrt{3}\Big]$

$\Big[-5\sqrt{3};-5\sqrt{2} \Big] = \Big[-\sqrt{75};-\sqrt{50}\Big]$

verificăm numărul:

$-\sqrt{32} < - \sqrt{27} < -\sqrt{25}$

$\iff -4\sqrt{2} < -3\sqrt{3} < -5$

$\implies -3\sqrt{3} \in \Big[-4\sqrt{2};-5\Big]$