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$\sqrt{ 3 } \left( \sqrt{ 6 } +1 \right) - \sqrt{ 2 } \left( 3+ \sqrt{ 3 } \right)$
$\sqrt{ 3 } - \sqrt{ 6 }$
Calculate the value
$\sqrt{ \color{#FF6800}{ 3 } } \left ( \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) - \sqrt{ 2 } \left ( 3 + \sqrt{ 3 } \right )$
$ $ Multiply each term in parentheses by $ \sqrt{ 3 }$
$\sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } - \sqrt{ 2 } \left ( 3 + \sqrt{ 3 } \right )$
$\sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 3 } \times 1 - \sqrt{ 2 } \left ( 3 + \sqrt{ 3 } \right )$
$ $ Calculate multiplication of root $ $
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 3 } \times 1 - \sqrt{ 2 } \left ( 3 + \sqrt{ 3 } \right )$
$3 \sqrt{ 2 } + \sqrt{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } - \sqrt{ 2 } \left ( 3 + \sqrt{ 3 } \right )$
$ $ Multiplying any number by 1 does not change the value $ $
$3 \sqrt{ 2 } + \sqrt{ 3 } - \sqrt{ 2 } \left ( 3 + \sqrt{ 3 } \right )$
$3 \sqrt{ 2 } + \sqrt{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$ $ Multiply each term in parentheses by $ - \sqrt{ 2 }$
$3 \sqrt{ 2 } + \sqrt{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } }$
$3 \sqrt{ 2 } + \sqrt{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } - \sqrt{ 2 } \sqrt{ 3 }$
$ $ Simplify the expression $ $
$3 \sqrt{ 2 } + \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 2 } \sqrt{ 3 }$
$3 \sqrt{ 2 } + \sqrt{ 3 } - 3 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } }$
$ $ Calculate multiplication $ $
$3 \sqrt{ 2 } + \sqrt{ 3 } - 3 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } }$
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 6 }$
$ $ Eliminate opponent number $ $
$\sqrt{ 3 } - \sqrt{ 6 }$
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