Răspuns:
[tex]n = | \sqrt{1.(8) \times 0.2(6)} - \sqrt{2.25 \times 0.(3)} | \times (10 \sqrt{3} ) \\ n = | \sqrt{ \frac{18 - 1}{9} \times \frac{26 - 2}{90} } - \sqrt{ \frac{225}{100} \times \frac{3}{9} } | \times 10 \sqrt{3} \\ n = | \sqrt{ \frac{17}{9} \times \frac{24}{90} } - \sqrt{ \frac{225}{100} } \times \sqrt{ \frac{3}{9} } | \times 10 \sqrt{3} \\ n = | \sqrt{ \frac{17}{9} \times \frac{4}{15} } - \frac{ \sqrt{225} }{ \sqrt{100} } \times \frac{ \sqrt{3} }{ \sqrt{9} } | \times 10 \sqrt{3} \\ n = | \sqrt{ \frac{68}{135} } - \frac{15}{10} \times \frac{ \sqrt{3} }{3} | \times 10 \sqrt{3} \\ n = | \frac{ \sqrt{68} }{ \sqrt{135} } - \frac{15 \sqrt{3} }{30} | \times 10 \sqrt{3} \\ n = | \frac{2 \sqrt{17} }{3 \sqrt{15} } - \frac{ \sqrt{3} }{2} | \times 10 \sqrt{3} \\ n = | \frac{4 \sqrt{17} }{6 \sqrt{15} } - \frac{ \sqrt{3} \times 3 \sqrt{15} }{6 \sqrt{15} } | \times 10 \sqrt{3} \\ n = | \frac{4 \sqrt{17} }{6 \sqrt{15} } - \frac{3 \sqrt{45} }{6 \sqrt{15} } | \times 10 \sqrt{3} \\ n = | \frac{4 \sqrt{17} - 3 \sqrt{45} }{6 \sqrt{15} } | \times 10 \sqrt{3} \\ cum \: \sqrt{17} < \sqrt{45} rezulta \: ca \: | \frac{4 \sqrt{17} - 3 \sqrt{45} }{6 \sqrt{15} } | < 0 \\ n = - ( \frac{4 \sqrt{17} - 3 \sqrt{45} }{6 \sqrt{15} }) \times 10 \sqrt{3} \\ n = - ( \frac{40 \sqrt{51} - 30 \sqrt{135} }{6 \sqrt{15} } ) \\ n = \frac{40 \sqrt{51} - 30 \times 3 \sqrt{15} }{6 \sqrt{15} } \\ n = \frac{40 \sqrt{51} - 90 \sqrt{15} }{6 \sqrt{15} } \\ n = \frac{40 \sqrt{51} }{6 \sqrt{15} } - \frac{90 \sqrt{15} }{6 \sqrt{15} } \\ n = \frac{20}{3} \times \frac{ \sqrt{17} }{ \sqrt{5} } - 15 \\ n = \frac{20 \sqrt{17} }{3 \sqrt{5} } - 15[/tex]
