Explicație pas cu pas:
a)
[tex]\Big( \frac{ ^{2 \sqrt{3})} 1}{ \sqrt{3} } + \frac{^{2}2 \sqrt{3} }{3} + \frac{ ^{\sqrt{6})}\sqrt{2} }{ \sqrt{6} } \Big) \cdot \frac{3}{ \sqrt{48} } = \\ = \frac{2 \sqrt{3} + 4 \sqrt{3} + 2 \sqrt{3} }{6} \cdot \frac{3}{ 4\sqrt{3} } \\ = \frac{8 \sqrt{3}}{6} \cdot \frac{3}{ 4\sqrt{3} } = \frac{24 \sqrt{3} }{24 \sqrt{3} } = \bf 1[/tex]
b)
[tex]\frac{ \sqrt{3} + \sqrt{12} + \sqrt{27} + ... + \sqrt{300} }{ \sqrt{5} + \sqrt{20} + \sqrt{45} + ... + \sqrt{500}} = \\ = \frac{ \sqrt{3} \cdot (1 + \sqrt{4} + \sqrt{9} + ... + \sqrt{100} }{ \sqrt{5} \cdot (1 + \sqrt{4} + \sqrt{9} + ... + \sqrt{100})} \\ = \frac{ \sqrt{3} }{ \sqrt{5} } = \bf \sqrt{ \frac{3}{5} } = \frac{ \sqrt{15} }{5} [/tex]
