Question

136 задание!!!! Срочно

Answer 1

Ответ:

а) $2 \sqrt{5}$

б) $- \frac{4 \sqrt{10} }{5}$

в) $21$

г) $4$

Объяснение:

а)

$2 \sqrt{20} - 3 \sqrt{45} + 3 \sqrt{80} - \sqrt{125} = \\ \small = 2 \sqrt{5 \cdot4} - 3 \sqrt{5 \cdot9} + 3 \sqrt{5 \cdot16} - \sqrt{5 \cdot25} = \\ \small { =} 2 \sqrt{5} {\cdot} \sqrt{4} { -} 3 \sqrt{5} {\cdot} \sqrt{9} {+} 3\sqrt{5} {\cdot} \sqrt{16} {-} \sqrt{5} {\cdot} \sqrt{25} {= } \\ \small = 2{ \cdot}2 \sqrt{5} - 3{ \cdot}3\sqrt{5} + 3{ \cdot}4 \sqrt{5} - 5 \sqrt{5} = \\ \small = 4 \sqrt{5} - 9 \sqrt{5} + 12 \sqrt{5} - 5 \sqrt{5} = \\ \small = \sqrt{5} \cdot (4 - 9 + 12 - 5) = \sqrt{5} \cdot{2} = 2 \sqrt{5}$

б)

$10 \sqrt{ \frac{2}{5} } - 0.5 \sqrt{160} + 3 \sqrt{1\frac{1}{9} } = \\ \small = 10 \sqrt{ \frac{2{ \cdot}5}{5{\cdot}5} } - 0.5 \sqrt{16{\cdot}10} + 3 \sqrt{\frac{9{ + }1}{9} } = \\ \small = \frac{ \sqrt{10}}{ \sqrt{25} }- 0.5 \sqrt{16}{\cdot} \sqrt{10} + 3 \cdot{\frac{ \sqrt{10}}{ \sqrt{9}} } = \\ \small = \frac{ \sqrt{10}}{ 5 }- 0.5 {\cdot}4 {\cdot} \sqrt{10} + {\frac{ 3\sqrt{10}}{ 3} } = \\ = \sqrt{10} \: \Big( \frac{1}{5} -0.5{ \cdot \: }4 + \frac{3}{3} \Big) = \\ = \sqrt{10} (0.2 - 2 + 1) = - 0.8 \sqrt{10} = \\ = - \frac{4 \sqrt{10} }{5}$

в)

$( \sqrt{15} - \sqrt{6} )^{2} + 6 \sqrt{10} = \\ = {( \sqrt{15}) }^{2} {+} {( \sqrt{6}) }^{2}{ -} 2 \sqrt{15} \sqrt{6} {+} 6 \sqrt{10} = \\ = 15 + 6 -2 \sqrt{(5 {\cdot}3) \cdot(2 {\cdot}3) \: } {+} 6 \sqrt{10} = \\ = 21 -2 \sqrt{3 {\cdot}3 \cdot5 {\cdot}2 \: } {+} 6 \sqrt{10} = \\ = 21 -2 \sqrt{9}{ \cdot }\sqrt {10 \: } {+} 6 \sqrt{10} = \\ = 21 - 6 \sqrt{10 \: } + 6 \sqrt{10 \: } = 21$

г)

$\Big( \frac{3}{ \sqrt{3} } + \frac{7}{ \sqrt{7} } \Big) {\cdot}( \sqrt{7} - \sqrt{3} ) = \\ \small {= \Big( \frac{ ({ \sqrt{3} })^{2} }{ \sqrt{3} } + \frac{ {( \sqrt{7}) }^{2} }{ \sqrt{7} } \Big) }{\cdot}( \sqrt{7} - \sqrt{3} ) = \\ \small = ( \sqrt{3} { +} \sqrt{7} )( \sqrt{7} {-} \sqrt{3} ) = ( \sqrt{7} )^{2} {- } {( \sqrt{3} )}^{2} = \\ = 7 - 3 = 4$