Răspuns:
[tex]\boxed{\bf \frac{55 \sqrt{3} }{36} }[/tex]
Explicație pas cu pas:
[tex]\bf{( \frac{1}{ \sqrt{3} } ) {}^{ 3} + \frac{ \sqrt{27} }{ \sqrt{8} } \div \frac{1}{ \sqrt{2} } - \sqrt{0.1(6)} \div (2 \sqrt{2} ) }[/tex]
primul pas este sa transformam fractia zecimala periodica 0,1(6) in fractie ordinara
[tex]\bf{( \frac{1}{ \sqrt{3} }) {}^{3} + \frac{ \sqrt{27} }{ \sqrt{8} } \div \frac{1}{ \sqrt{2} } - \sqrt{ \frac{16 - 1}{90} } \div (2 \sqrt{2} )}[/tex]
[tex]\bf{(3 {}^{ - \frac{1}{2} } ) {}^{3} + \frac{ \sqrt{27} }{ \sqrt{\not8} } \times \sqrt{\not2} - \sqrt{ \frac{15}{90} } \div (2 \sqrt{2} ) }[/tex]
[tex]\bf{am \: transformat \: ( \frac{1}{ \sqrt{3} } ) {}^{3} \: in \: (3 {}^{ - \frac{1}{2} }) {}^{3} \: folosind \: \frac{1}{ \sqrt[n]{a {}^{m} } } = a {}^{ - \frac{m}{n} } }[/tex]
[tex]\bf{ ⋆ \: 3 {}^{ - \frac{3}{2} } + \frac{ \sqrt{27} }{ \sqrt{4} } - \frac{ \sqrt{ \frac{\not15}{\not90} {}^{(15} } }{2 \sqrt{2} } = \frac{1}{3 {}^{ \frac{3}{2} } } + \frac{3 \sqrt{3} }{2} - \frac{ \sqrt{ \frac{1}{6} } }{2 \sqrt{2} } }[/tex]
[tex]\bf{ ⋆ \frac{1}{ \sqrt{3 {}^{3} } } + \frac{ 3\sqrt{3} }{2} - \frac{ \frac{1}{ \sqrt{6} } }{2 \sqrt{2} } = \frac{1}{3 \sqrt{3} } + \frac{3 \sqrt{3} }{2} - \frac{1}{2 \sqrt{12} } }[/tex]
[tex]\bf{ ⋆ \frac{ \sqrt{3} }{9} + \frac{3 \sqrt{3} }{2} - \frac{1}{4 \sqrt{3} } = {}^{4)} \frac{ \sqrt{3} }{9} + {}^{18)} \frac{3 \sqrt{3} }{2} - {}^{3)} \frac{ \sqrt{3} }{12} }[/tex]
aducem la acelasi numitor comun amplificand fractiile
[tex]\bf{⋆ \frac{4 \sqrt{3} }{4 \times 9} + \frac{18 \times 3 \sqrt{3} }{18 \times 2} - \frac{3 \sqrt{3} }{3 \times 12} = \frac{4 \sqrt{3} }{36} + \frac{54 \sqrt{3} }{36} - \frac{3 \sqrt{3} }{36} =\boxed{\bf \frac{55 \sqrt{3} }{36} } }[/tex]
Daca esti de pe telefon gliseaza spre dreapta pentru a vedea rezolvarea completa
Bafta ! :)
