Question

calculati dau coroana

Answer 1

Răspuns:

a) $\sqrt{4\sqrt{2} \cdot25\sqrt{8} }$

$=\sqrt{4\sqrt{2} \cdot25\cdot2\sqrt{2} } \\\\=\sqrt{4\cdot2\cdot25\cdot2} \\\\=\sqrt{400} \\\\\boxed{=20}$

b) $\sqrt{10\sqrt{15} : (2\sqrt{5}) \cdot 125\sqrt{27} }$

$=\sqrt{\sqrt{3}\cdot125\cdot3\sqrt{3} } \\\\=\sqrt{5\cdot3\cdot125\cdot3} \\\\ =\sqrt{5625} \\\\\boxed{=75}$

c) $\sqrt{2\sqrt{3}:(4\sqrt{6})\cdot18\sqrt{2} \cdot\sqrt{6} \cdot9\sqrt{6} }$

$=\sqrt{\frac{2\sqrt{3} }{4\sqrt{6} } \cdot18\sqrt{2}\cdot6\cdot9} \\\\=\sqrt{\frac{1}{2\sqrt{2} } \cdot18\sqrt{2}\cdot6\cdot9} \\\\=\sqrt{1\cdot9\cdot6\cdot9} \\\\=\sqrt{486} \\\\\boxed{=9\sqrt{6}}$

d) $\sqrt{\frac{12\sqrt{6}}{3}\cdot \frac{\sqrt{6}}{9}\cdot6^{-1} }$

$=\sqrt{4\sqrt{6}\cdot\frac{\sqrt{6}}{9}\cdot6^{-1} } \\\\=\sqrt{\frac{4\sqrt{6}\cdot\sqrt{6}\cdot6^{-1}}{9} } \\\\=\sqrt{\frac{4\cdot6^{1}\cdot6^{-1}}{9} } \\\\=\sqrt{\frac{4\cdot6^{1-1}}{9} } \\\\=\sqrt{\frac{4\cdot6^{0}}{9} } \\\\=\sqrt{\frac{4}{9} } \\\\\boxed{=\frac{2}{3} }$

Sper ca te-am ajutat!