Question

Ajutor ,ofer coroana
Repede !!!

Answer 1

Explicație pas cu pas:

a=$2\sqrt{2} (\sqrt{8} -3\sqrt{18} +2\sqrt{50} )$

a=$2\sqrt{2} (2\sqrt{2} -3*3\sqrt{2} + 2*5\sqrt{2} )$

a=$2\sqrt{2} (2\sqrt{2} -9\sqrt{2} +10\sqrt{2} )$

a=$2\sqrt{2} * 3\sqrt{2}$

a=$6\sqrt{4}$

a=12

$8\sqrt{2$≈11,31

$8\sqrt{3}$≈13,85

⇒ 11,31 < 12 < 13,85 ⇒ $8\sqrt{2}$ < a < $8\sqrt{3}$ ⇒ a∈($8\sqrt{2$,$8\sqrt{3}$)

b=($\frac{2}{5\sqrt{3} } + \frac{5}{2\sqrt{3} }$)*$\sqrt{300} -\sqrt{4}$

b=($\frac{4}{10\sqrt{3} } + \frac{25}{10\sqrt{3} }$)*$10\sqrt{3}$$-\sqrt{4}$

b=$\frac{29}{10\sqrt{3} }$*$10\sqrt{3}$$-\sqrt{4$

b=29-2

b=27

⇒$\sqrt{\frac{a}{b} } = \sqrt{\frac{12}{27} }= \frac{\sqrt{12} }{\sqrt{27} } = \frac{2\sqrt{3} }{3\sqrt{3} } = \frac{2}{3}$ ∈ R (rational)