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$6 \sqrt{ 2 } - 4$
Calculate the value
$\sqrt{ 2 } \left ( 3 - \sqrt{ \color{#FF6800}{ 32 } } \right ) + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\sqrt{ 2 } \left ( 3 - \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$\sqrt{ 2 } \left ( 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$ $ Get rid of unnecessary parentheses $ $
$\sqrt{ 2 } \left ( 3 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$ $ Multiply each term in parentheses by $ \sqrt{ 2 }$
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \sqrt{ 2 } \left ( - 4 \sqrt{ 2 } \right ) + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \left ( - 4 \sqrt{ 2 } \right ) + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$3 \sqrt{ 2 } + \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$ $ Get rid of unnecessary parentheses $ $
$3 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$3 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$ $ Simplify the expression $ $
$3 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } + \left ( \sqrt{ 48 } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$3 \sqrt{ 2 } - 8 + \left ( \sqrt{ \color{#FF6800}{ 48 } } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$3 \sqrt{ 2 } - 8 + \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 54 } \right ) \div \sqrt{ 3 }$
$3 \sqrt{ 2 } - 8 + \left ( 4 \sqrt{ 3 } + \sqrt{ \color{#FF6800}{ 54 } } \right ) \div \sqrt{ 3 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$3 \sqrt{ 2 } - 8 + \left ( 4 \sqrt{ 3 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \div \sqrt{ 3 }$
$3 \sqrt{ 2 } - 8 + \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \color{#FF6800}{ \div } \sqrt{ \color{#FF6800}{ 3 } }$
$ $ Present division as a fraction $ $
$3 \sqrt{ 2 } - 8 + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } } } { \sqrt{ \color{#FF6800}{ 3 } } } }$
$3 \sqrt{ 2 } - 8 + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } } } { \sqrt{ \color{#FF6800}{ 3 } } } }$
$ $ Calculate the expression $ $
$3 \sqrt{ 2 } - 8 + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 12 } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 3 } } }$
$3 \sqrt{ 2 } - 8 + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 12 } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 3 } } }$
$ $ Reduce the fraction $ $
$3 \sqrt{ 2 } - 8 + \color{#FF6800}{ 4 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } - 8 + 4 \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } - 8 + 4$
$6 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$ $ Add $ - 8 $ and $ 4$
$6 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
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