Question

Comparati următoarele numere reale

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Answer 1

Răspuns:

$a)2 \sqrt{5} = \sqrt{ {2}^{2} \times 5 } = \sqrt{20 } \\ 3 \sqrt{2} = \sqrt{ {3}^{2} \times 2 } = \sqrt{18} \\ \sqrt{20} > \sqrt{18} \\ 2 \sqrt{5} > 3 \sqrt{2} \\ b)4 \sqrt{2} = \sqrt{ {4}^{2} \times 2 } = \sqrt{32} \\ 3 \sqrt{5} = \sqrt{ { 3}^{2} \times 5} = \sqrt{45} \\ \sqrt{32} < \sqrt{45} \\ 4 \sqrt{2} < 3 \sqrt{5} \\ c)2 \sqrt{6} = \sqrt{ {2}^{2} \times 6 } = \sqrt{24} \\ 3 \sqrt{3} = \sqrt{ {3}^{2} \times 3 } = \sqrt{27} \\ \sqrt{24} < \sqrt{27} \\ 2 \sqrt{6} < 3 \sqrt{3} \\ d)4 \sqrt{2} = \sqrt{ {4}^{2} \times 2 } = \sqrt{32} \\ 2 \sqrt{7} = \sqrt{ {2}^{2} \times 7 } = \sqrt{28} \\ \sqrt{32} > \sqrt{28 } \\ 4 \sqrt{2} > 2 \sqrt{7}$

$7)a) - 4 \sqrt{3} = \sqrt{( { - 4)}^{2} \times 3 } = \sqrt{48} \\ - 5 \sqrt{2} = \sqrt{ {( - 5)}^{2} \times 2 } = \sqrt{50} \\ \sqrt{48} < \sqrt{50} \\ - 4 \sqrt{3} < - 5 \sqrt{2} \\ b) - 2 \sqrt{11} = \sqrt{ {( - 2)}^{2} \times 11 } = \sqrt{44} \\ - 3 \sqrt{5} = \sqrt{ {( - 3)}^{2 } \times 5 } = \sqrt{45} \\ \sqrt{44} < \sqrt{45} \\ - 2 \sqrt{11} < - 3 \sqrt{5} \\c) - 4 \sqrt{5} = \sqrt{ {( - 4)}^{2} \times 5 } = \sqrt{80} \\ - 5 \sqrt{3} = \sqrt{ {( - 5)}^{2} \times 3 } = \sqrt{75} \\ \sqrt{80} > \sqrt{75} \\ - 4 \sqrt{5} > - 5 \sqrt{3} \\ d) - 4 \sqrt{6} = \sqrt{ {( - 4)}^{2} \times 6 } = \sqrt{96} \\ - 7 \sqrt{2} = \sqrt{( { - 7)}^{2} \times 2 } = \sqrt{98} \\ \sqrt{96} < \sqrt{98} \\ - 4 \sqrt{6} < - 7 \sqrt{2}$