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Answer
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$\sqrt{ 24 } \left( \dfrac{ 8 }{ \sqrt{ 3 } } - \sqrt{ 6 } \right) + \left( \sqrt{ 32 } -10 \right) \div \sqrt{ 2 }$
$11 \sqrt{ 2 } - 8$
Calculate the value
$\sqrt{ \color{#FF6800}{ 24 } } \left ( \dfrac { 8 } { \sqrt{ 3 } } - \sqrt{ 6 } \right ) + \left ( \sqrt{ 32 } - 10 \right ) \div \sqrt{ 2 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \left ( \dfrac { 8 } { \sqrt{ 3 } } - \sqrt{ 6 } \right ) + \left ( \sqrt{ 32 } - 10 \right ) \div \sqrt{ 2 }$
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \left ( \color{#FF6800}{ \dfrac { 8 } { \sqrt{ 3 } } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right ) + \left ( \sqrt{ 32 } - 10 \right ) \div \sqrt{ 2 }$
$ $ Expand the expression to calculate the value $ $
$\color{#FF6800}{ 16 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 12 } + \left ( \sqrt{ 32 } - 10 \right ) \div \sqrt{ 2 }$
$16 \sqrt{ 2 } - 12 + \left ( \sqrt{ \color{#FF6800}{ 32 } } - 10 \right ) \div \sqrt{ 2 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$16 \sqrt{ 2 } - 12 + \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } - 10 \right ) \div \sqrt{ 2 }$
$16 \sqrt{ 2 } - 12 + \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ \div } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Present division as a fraction $ $
$16 \sqrt{ 2 } - 12 + \color{#FF6800}{ \dfrac { 4 \sqrt{ 2 } - 10 } { \sqrt{ 2 } } }$
$16 \sqrt{ 2 } - 12 + \color{#FF6800}{ \dfrac { 4 \sqrt{ 2 } - 10 } { \sqrt{ 2 } } }$
$ $ Calculate the expression $ $
$16 \sqrt{ 2 } - 12 + \color{#FF6800}{ \dfrac { 8 - 10 \sqrt{ 2 } } { 2 } }$
$16 \sqrt{ 2 } - 12 + \color{#FF6800}{ \dfrac { 8 - 10 \sqrt{ 2 } } { 2 } }$
$ $ Reduce the fraction $ $
$16 \sqrt{ 2 } - 12 + \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 16 } \sqrt{ \color{#FF6800}{ 2 } } - 12 + 4 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 2 } } - 12 + 4$
$11 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$ $ Add $ - 12 $ and $ 4$
$11 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
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