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$\sqrt{ 2 } \left( 4 \sqrt{ 8 } + \sqrt{ 12 } \right) - \dfrac{ \sqrt{ 3 } \left( \sqrt{ 6 } -2 \right) }{ \sqrt{ 2 } }$
$13 + 3 \sqrt{ 6 }$
Calculate the value
$\sqrt{ 2 } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 8 } } + \sqrt{ 12 } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$ $ Simplify the expression $ $
$\sqrt{ 2 } \left ( \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 12 } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$\sqrt{ 2 } \left ( 8 \sqrt{ 2 } + \sqrt{ \color{#FF6800}{ 12 } } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\sqrt{ 2 } \left ( 8 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$ $ Multiply each term in parentheses by $ \sqrt{ 2 }$
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ 2 } \left ( 2 \sqrt{ 3 } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$ $ Get rid of unnecessary parentheses $ $
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \left ( 2 \sqrt{ 3 } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \left ( 2 \sqrt{ 3 } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 16 } + \sqrt{ 2 } \left ( 2 \sqrt{ 3 } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$16 + \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$ $ Get rid of unnecessary parentheses $ $
$16 + \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$16 + \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$ $ Simplify the expression $ $
$16 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } - \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } }$
$16 + 2 \sqrt{ 6 } - \color{#FF6800}{ \dfrac { \sqrt{ 3 } \left ( \sqrt{ 6 } - 2 \right ) } { \sqrt{ 2 } } }$
$ $ Calculate the expression $ $
$16 + 2 \sqrt{ 6 } - \color{#FF6800}{ \dfrac { 6 - 2 \sqrt{ 6 } } { 2 } }$
$16 + 2 \sqrt{ 6 } - \color{#FF6800}{ \dfrac { 6 - 2 \sqrt{ 6 } } { 2 } }$
$ $ Reduce the fraction $ $
$16 + 2 \sqrt{ 6 } - \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right )$
$16 + 2 \sqrt{ 6 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$16 + 2 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } + \sqrt{ \color{#FF6800}{ 6 } }$
$\color{#FF6800}{ 16 } + 2 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } + \sqrt{ 6 }$
$ $ Subtract $ 3 $ from $ 16$
$\color{#FF6800}{ 13 } + 2 \sqrt{ 6 } + \sqrt{ 6 }$
$13 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } }$
$ $ Calculate between similar terms $ $
$13 + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } }$
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