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$- \sqrt{ 6 } + 3 \sqrt{ 2 }$
Calculate the value
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) - \left ( \sqrt{ 24 } - \sqrt{ 50 } \right )$
$ $ Multiply each term in parentheses by $ \sqrt{ 2 }$
$\sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) - \left ( \sqrt{ 24 } - \sqrt{ 50 } \right )$
$\sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 2 } \left ( - 2 \right ) - \left ( \sqrt{ 24 } - \sqrt{ 50 } \right )$
$ $ Calculate multiplication of root $ $
$\sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 2 } \left ( - 2 \right ) - \left ( \sqrt{ 24 } - \sqrt{ 50 } \right )$
$\sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) - \left ( \sqrt{ 24 } - \sqrt{ 50 } \right )$
$ $ Simplify the expression $ $
$\sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } - \left ( \sqrt{ 24 } - \sqrt{ 50 } \right )$
$\sqrt{ 6 } - 2 \sqrt{ 2 } - \left ( \sqrt{ \color{#FF6800}{ 24 } } - \sqrt{ 50 } \right )$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\sqrt{ 6 } - 2 \sqrt{ 2 } - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } - \sqrt{ 50 } \right )$
$\sqrt{ 6 } - 2 \sqrt{ 2 } - \left ( 2 \sqrt{ 6 } - \sqrt{ \color{#FF6800}{ 50 } } \right )$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\sqrt{ 6 } - 2 \sqrt{ 2 } - \left ( 2 \sqrt{ 6 } - \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right )$
$\sqrt{ 6 } - 2 \sqrt{ 2 } - \left ( 2 \sqrt{ 6 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right )$
$ $ Get rid of unnecessary parentheses $ $
$\sqrt{ 6 } - 2 \sqrt{ 2 } - \left ( 2 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$\sqrt{ 6 } - 2 \sqrt{ 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$\sqrt{ 6 } - 2 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } + \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } }$
$\sqrt{ \color{#FF6800}{ 6 } } - 2 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } + 5 \sqrt{ 2 }$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 6 } } - 2 \sqrt{ 2 } + 5 \sqrt{ 2 }$
$- 1 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Calculate between similar terms $ $
$- 1 \sqrt{ 6 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ 6 } + 3 \sqrt{ 2 }$
$ $ Multiplying any number by 1 does not change the value $ $
$- \sqrt{ 6 } + 3 \sqrt{ 2 }$
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