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$\dfrac{ 3 }{ 2 \sqrt{ 3 } } \left( \sqrt{ 2 } - \sqrt{ 3 } \right) - \dfrac{ 2 \sqrt{ 3 } - \sqrt{ 8 } }{ \sqrt{ 2 } }$
$\dfrac { - \sqrt{ 6 } + 1 } { 2 }$
Calculate the value
$\color{#FF6800}{ \dfrac { 3 } { 2 \sqrt{ 3 } } } \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Calculate the expression $ $
$\color{#FF6800}{ \dfrac { 3 \sqrt{ 3 } } { 6 } } \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\color{#FF6800}{ \dfrac { 3 \sqrt{ 3 } } { 6 } } \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Reduce the fraction $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Multiply each term in parentheses by $ \dfrac { \sqrt{ 3 } } { 2 }$
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Arrange the terms multiplied by fractions $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } \sqrt{ 2 } } { 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } } { 2 } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Calculate multiplication of root $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } } { 2 } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( \color{#FF6800}{ - } \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Move the (-) sign forward $ $
$\dfrac { \sqrt{ 6 } } { 2 } \color{#FF6800}{ - } \dfrac { \sqrt{ 3 } } { 2 } \sqrt{ 3 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \sqrt{ \color{#FF6800}{ 3 } } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Arrange the terms multiplied by fractions $ $
$\dfrac { \sqrt{ 6 } } { 2 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \sqrt{ 3 } \sqrt{ 3 } } { 2 } } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ 3 } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ 3 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 3 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ 3 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Add the exponent as the base is the same $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Add $ 1 $ and $ 1$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ If you square the radical sign, it will disappear $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \color{#FF6800}{ 3 } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { 3 } { 2 } - \color{#FF6800}{ \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } } }$
$ $ Calculate the expression $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { 3 } { 2 } - \color{#FF6800}{ \dfrac { 2 \sqrt{ 6 } - \left ( 2 \sqrt{ 2 } \right ) \sqrt{ 2 } } { 2 } }$
$\color{#FF6800}{ \dfrac { \sqrt{ 6 } } { 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 \sqrt{ 6 } - \left ( 2 \sqrt{ 2 } \right ) \sqrt{ 2 } } { 2 } }$
$ $ Combine the fraction with the same denominator $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 2 }$
$\dfrac { \sqrt{ 6 } - 3 - \left ( 2 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 2 }$
$ $ Simplify the expression $ $
$\dfrac { \sqrt{ 6 } - 3 - \left ( 2 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) } { 2 }$
$\dfrac { \sqrt{ 6 } - 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) } { 2 }$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$\dfrac { \sqrt{ 6 } - 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } + \color{#FF6800}{ 4 } } { 2 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } - 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } + 4 } { 2 }$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 6 } } - 3 + 4 } { 2 }$
$\dfrac { - 1 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } } { 2 }$
$ $ Add $ - 3 $ and $ 4$
$\dfrac { - 1 \sqrt{ 6 } + \color{#FF6800}{ 1 } } { 2 }$
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ 6 } + 1 } { 2 }$
$ $ Multiplying any number by 1 does not change the value $ $
$\dfrac { - \sqrt{ 6 } + 1 } { 2 }$
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