Question

(5p) 4. Cel mai mic număr natural n pentru care 3√ne (2√5, 4√3) este:
a) 0; b) 1; c) 4; 2 d) 5. 5x4​

Answer 1

Răspuns:

c) 4

Explicație pas cu pas:

$2 \sqrt{5} = \sqrt{20} \iff \sqrt{16} < \sqrt{20} < \sqrt{25} \\4 < \sqrt{20} < 5 \implies 4 < 2 \sqrt{5} < 5$

$4 \sqrt{3} = \sqrt{48} \iff \sqrt{36} < \sqrt{48} < \sqrt{49} \\6 < \sqrt{48} < 7 \implies 6 < 4 \sqrt{3} < 7$

$\implies 4 < {\bf 2 \sqrt{5} < 5 < 6 < 4 \sqrt{3}} < 7$

$3 \sqrt{0} = 3 \cdot 0 = 0 \\ 3 \sqrt{1} = 3 \cdot 1 = 3 \\ 3 \sqrt{4} = 3 \cdot 2 = 6$

$3 \sqrt{5} = \sqrt{30} \iff \sqrt{25} < \sqrt{30} < \sqrt{36} \\5 < \sqrt{30} < 6 \implies 5 < 3 \sqrt{5} < 6$

deoarece:

$3 \sqrt{4} < 3 \sqrt{5}$

=> cel mai mic număr natural n este 4