Explicație pas cu pas:
[tex]a) \frac{2 \sqrt{6} }{ \sqrt{3} } = \frac{2 \sqrt{6} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{2 \sqrt{6} \sqrt{3} }{3} = \frac{2 \sqrt{18} }{3} = \frac{2 \times 3 \sqrt{2} }{3} = \frac{6 \sqrt{2} }{3} = 2 \sqrt{2} [/tex]
[tex]b) \frac{ - 7 \sqrt{13} }{ \sqrt{26} } = \frac{ - 7 \sqrt{13} }{ \sqrt{26} } \times \frac{ \sqrt{26} }{ \sqrt{26} } = \frac{ - 7 \sqrt{13} \sqrt{26} }{26} = \frac{ - 7 \sqrt{13 \times 26} }{26} = \frac{ - 7 \sqrt{338} }{26} = \frac{ - 7 \times 13 \sqrt{2} }{26} = \frac{ - 91 \sqrt{2} }{26} = - \frac{91 \sqrt{2} }{26} ^{(13} = - \frac{7 \sqrt{2} }{2} [/tex]
[tex]c) \frac{4 \sqrt{10} }{ - \sqrt{24} } = \frac{4 \sqrt{10} }{ - 2 \sqrt{6} } = \frac{4 \sqrt{10} }{ - 2 \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } = \frac{4 \sqrt{10} \sqrt{6} }{ - 2 \times 6} = \frac{4 \sqrt{60} }{ - 12} = \frac{4 \times 2 \sqrt{15} }{ - 12} = \frac{8 \sqrt{15} }{ - 12} = - \frac{8 \sqrt{15} }{12} ^{(4} = - \frac{2 \sqrt{15} }{3} [/tex]
[tex]d) \frac{15}{2 \sqrt{60} } = \frac{15}{2 \times 2 \sqrt{15} } = \frac{15}{4 \sqrt{15} } \times \frac{ \sqrt{15} }{ \sqrt{15} } = \frac{15 \sqrt{15} }{4 \times 15} = \frac{15 \sqrt{15} }{60} ^{(15} = \frac{ \sqrt{15} }{4} [/tex]
