Question

calculati: a) (5√2/2√5 + 3/√10) • (√10)^-1; b) (2/5√3 - 1/√12 + 3/√75) c) √2 - 1/√2 + √3 - √2/√6 + √4 - √3/√12​

Answer 1

Explicație pas cu pas:

a)

$\bigg( \dfrac{5 \sqrt{2}^{( \sqrt{5} } }{2 \sqrt{5} } + \dfrac{3 ^{( \sqrt{10} } }{ \sqrt{10} } \bigg) \cdot {( \sqrt{10} )}^{ - 1} = \bigg( \dfrac{5 \sqrt{10} }{2 \cdot 5} + \dfrac{3 \sqrt{10} }{10} \bigg) \cdot \dfrac{1}{ \sqrt{10}} = \dfrac{8 \sqrt{10} }{10} \cdot \dfrac{1}{ \sqrt{10}} = \dfrac{8}{10} = \dfrac{4}{5}$

b)

$\dfrac{2}{5 \sqrt{3} } - \dfrac{1}{\sqrt{12} } + \dfrac{3}{\sqrt{75} } = \dfrac{2^{(2\sqrt{3} } }{5 \sqrt{3} } - \dfrac{1^{(5\sqrt{3}}}{2\sqrt{3} } + \dfrac{3^{(2\sqrt{3}}}{5\sqrt{3} } = \dfrac{4 \sqrt{3} - 5 \sqrt{3} + 6 \sqrt{3} }{30} = \dfrac{5 \sqrt{3} }{30} = \dfrac{\sqrt{3} }{6}$

c)

$\sqrt{2} - \dfrac{1^{( \sqrt{2} } }{ \sqrt{2} } + \sqrt{3} - \dfrac{ \sqrt{2}^{( \sqrt{6} } }{ \sqrt{6} } + \sqrt{4} - \dfrac{ \sqrt{3} }{ \sqrt{12} } = \sqrt{2} - \dfrac{ \sqrt{2} }{2} + \sqrt{3} - \dfrac{ 2\sqrt{3} }{6} + 2 - \dfrac{ \sqrt{3} }{2\sqrt{3} } = \dfrac{ 2\sqrt{2} }{2} - \dfrac{ \sqrt{2} }{2} + \dfrac{ 3\sqrt{3} }{3} - \dfrac{ \sqrt{3} }{3} + \dfrac{4}{2} - \dfrac{1}{2} = \dfrac{ \sqrt{2} }{2} + \dfrac{ 2\sqrt{3} }{3} + \dfrac{3}{2} = \dfrac{ 3\sqrt{2} + 4 \sqrt{3} + 9}{6}$