Question

11.a) Ordonaţi descrescator numerele: a=5√2, b=2√√13, c=4√3. b) Ordonaţi crescator numerele a = √√8-√√50-√√18, b= -√√12-√√27 sic= -√√74.​

Answer 1

Explicație pas cu pas:

a)

$a = 5 \sqrt{2} = \sqrt{ {5}^{2} \cdot 2 } = \sqrt{50} \: \: \: \: \\ b = 2 \sqrt{13} = \sqrt{ {2}^{2} \cdot 13 } = \sqrt{52} \\ c = 4 \sqrt{3} = \sqrt{ {4}^{2} \cdot 3 } = \sqrt{48} \: \: \: \:$

$\sqrt{52} > \sqrt{50} > \sqrt{48}$

$\implies b > a > c$

b)

$a = \sqrt{8} - \sqrt{50} - \sqrt{18} = 2 \sqrt{2} - 5 \sqrt{2} - 3 \sqrt{2} = - 6 \sqrt{2} = - \sqrt{72}$

$b = - \sqrt{12} - \sqrt{27} = - 2 \sqrt{3} - 3 \sqrt{3} = - 5 \sqrt{3} = - \sqrt{75}$

$c = - \sqrt{74}$

$- \sqrt{75} < - \sqrt{74} < - \sqrt{72}$

$\implies b < c < a$