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$- 2 \sqrt{ 6 } + 3$
Calculate the value
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } } { \sqrt{ \color{#FF6800}{ 3 } } } } + \left ( 2 \sqrt{ 2 } - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$ $ Calculate the expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 3 } } } + \left ( 2 \sqrt{ 2 } - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$\dfrac { 3 \sqrt{ 6 } - \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } } { 3 } + \left ( 2 \sqrt{ 2 } - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$ $ If you square the radical sign, it will disappear $ $
$\dfrac { 3 \sqrt{ 6 } - \color{#FF6800}{ 3 } } { 3 } + \left ( 2 \sqrt{ 2 } - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } } { \color{#FF6800}{ 3 } } } + \left ( 2 \sqrt{ 2 } - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$ $ Reduce the fraction $ $
$\sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } + \left ( 2 \sqrt{ 2 } - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$\sqrt{ 6 } - 1 + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Multiply each term in parentheses by $ \sqrt{ 2 }$
$\sqrt{ 6 } - 1 + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \sqrt{ \color{#FF6800}{ 2 } }$
$\sqrt{ 6 } - 1 + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$ $ Get rid of unnecessary parentheses $ $
$\sqrt{ 6 } - 1 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$\sqrt{ 6 } - 1 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$ $ Simplify the expression $ $
$\sqrt{ 6 } - 1 + \color{#FF6800}{ 4 } + \left ( - 3 \sqrt{ 3 } \right ) \sqrt{ 2 }$
$\sqrt{ 6 } - 1 + 4 + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Get rid of unnecessary parentheses $ $
$\sqrt{ 6 } - 1 + 4 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } }$
$\sqrt{ 6 } - 1 + 4 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Simplify the expression $ $
$\sqrt{ 6 } - 1 + 4 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } }$
$\sqrt{ \color{#FF6800}{ 6 } } - 1 + 4 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } }$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } - 1 + 4$
$- 2 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$ $ Add $ - 1 $ and $ 4$
$- 2 \sqrt{ 6 } + \color{#FF6800}{ 3 }$
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