Question

v6(3v3/4v2)+v24(5/v2-7/v3)+v50

Answer 1

Explicație pas cu pas:

$\sqrt{6} \cdot \dfrac{3\sqrt{3} }{4 \sqrt{2} } + \sqrt{24} \cdot \bigg(\dfrac{5}{ \sqrt{2} } - \dfrac{7}{ \sqrt{3} } \bigg) + \sqrt{50} =$

$= \dfrac{3\sqrt{18} }{4 \sqrt{2} } + \dfrac{5\sqrt{24}}{ \sqrt{2} } - \dfrac{7\sqrt{24}}{ \sqrt{3} } + \sqrt{2 \cdot {5}^{2} }$

$= \dfrac{3\sqrt{9} }{4} + 5\sqrt{12} - 7\sqrt{8} + \sqrt{2 \cdot {5}^{2} }$

$= \dfrac{ {3}^{2} }{4} + 5 \sqrt{ {2}^{2} \cdot 3} - 7 \sqrt{ {2}^{3} } + 5\sqrt{2}$

$= \dfrac{9}{4} + 10 \sqrt{3} - 14 \sqrt{2} + 5\sqrt{2}$

$= \dfrac{9}{4} + 10 \sqrt{3} - 9 \sqrt{2}$