Question

$\frac{6 \sqrt{20} }{7 \sqrt{5} } xx ( \frac{3}{2 \sqrt{54} } + \sqrt{0,1(6)} - \frac{5}{ \sqrt{6} } )$

unde e ''xx'' este inmultire

Answer 1

$\it \dfrac{6\sqrt{20}}{7\sqrt5}\cdot \left(\dfrac{3}{2\sqrt{54}} +\sqrt{0,1(6)} -\dfrac{5}{\sqrt6}\right)$


[tex]\it \sqrt{20}=\sqrt{4\cdot5} =2\sqrt5 \\\;\\ \sqrt{54}=\sqrt{9\cdot6} =3\sqrt6 \\\;\\ \sqrt{0,1(6)} =\sqrt{\dfrac{16-1}{90}=\sqrt{15}{90}}=\sqrt{\dfrac{1}{6}}=\dfrac{1}{\sqrt6}[/tex]

Acum, exercițiul devine:

[tex]\it\dfrac{6\cdot2\sqrt5}{7\sqrt5} \cdot\left(\dfrac{3}{2\cdot3\sqrt6}+\dfrac{1}{\sqrt6}-\dfrac{5}{\sqrt6}\right) =\dfrac{6\cdot2}{7}\cdot\left(\dfrac{1}{2\sqrt6}-\dfrac{4}{\sqrt6}\right) = \\\;\\ \\\;\\ = \dfrac{6\cdot2}{7}\cdot\dfrac{-7}{2\sqrt6}=-\dfrac{6}{\sqrt6} =-\dfrac{\sqrt6\cdot \sqrt6}{\sqrt6} =-\sqrt6[/tex]