Question

va rog frumos si va inplor ma ajutati cu exercitiile la mate care sunt cu portocaliu? va rog frumos ​

Answer 1

Explicație pas cu pas:

$\dfrac{10}{ \sqrt{5} } = \dfrac{10 \sqrt{5} }{5} = 2 \sqrt{5}$

$\dfrac{2}{ \sqrt{5} } = \dfrac{2 \sqrt{5} }{5}$

$\dfrac{1}{ \sqrt{3} } = \dfrac{ \sqrt{3} }{3}$

$\dfrac{8}{ \sqrt{6} } = \dfrac{8 \sqrt{6} }{6} = \dfrac{4 \sqrt{6} }{3}$

.

$\dfrac{18}{ \sqrt{72} } = \dfrac{18}{ 6\sqrt{2} } = \dfrac{3}{\sqrt{2} } = \dfrac{3 \sqrt{2} }{2}$

$\dfrac{10}{ \sqrt{75} } = \dfrac{10}{ 5\sqrt{3} } = \dfrac{2}{\sqrt{3} } = \dfrac{2 \sqrt{3} }{3}$

.

$\dfrac{1}{ \sqrt{2} } + \dfrac{1}{ \sqrt{8} } + \dfrac{1}{\sqrt{18} } + \dfrac{1}{ \sqrt{32} } + \dfrac{1}{ \sqrt{50} } = \\ = \dfrac{1}{ \sqrt{2} } + \dfrac{1}{ 2\sqrt{2} } + \dfrac{1}{3\sqrt{2} } + \dfrac{1}{ 4\sqrt{2} } + \dfrac{1}{ 5\sqrt{2} } \\ = \dfrac{60 + 30 + 20 + 15 + 12}{60 \sqrt{2} } = \dfrac{137}{ 60\sqrt{2} } = \dfrac{137 \sqrt{2} }{120}$

$\dfrac{1}{ \sqrt{2}} \cdot \dfrac{1}{ \sqrt{8} } \cdot \dfrac{1}{\sqrt{18} } \cdot \dfrac{1}{ \sqrt{32} } \cdot \dfrac{1}{ \sqrt{50} } = \\ = \dfrac{1}{ \sqrt{2} } \cdot \dfrac{1}{ 2\sqrt{2} } \cdot \dfrac{1}{3\sqrt{2} } \cdot \dfrac{1}{ 4\sqrt{2} } \cdot \dfrac{1}{ 5\sqrt{2} } \\ = \dfrac{1}{ 2 \cdot 3 \cdot 4 \cdot 5 \cdot {( \sqrt{2} )}^{5}} = \dfrac{1}{120 \cdot 4 \sqrt{2} } \\ = \dfrac{1}{480 \sqrt{2} } = \dfrac{ \sqrt{2} }{480 \cdot 2} = \dfrac{ \sqrt{2} }{960}$