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$\sqrt{ 2 } \left( \sqrt{ 3 } - \sqrt{ 2 } \right) - \sqrt{ 3 } \left( \sqrt{ 3 } + \sqrt{ 2 } \right)$
$- 5$
Calculate the value
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$ $ Multiply each term in parentheses by $ \sqrt{ 2 }$
$\sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$\sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$ $ Calculate multiplication of root $ $
$\sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right ) - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$\sqrt{ 6 } + \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \sqrt{ 2 } \right ) - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$ $ Move the (-) sign forward $ $
$\sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ 2 } \sqrt{ 2 } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$\sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ 2 } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\sqrt{ 6 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 2 } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$\sqrt{ 6 } - \left ( \sqrt{ 2 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\sqrt{ 6 } - \left ( \sqrt{ 2 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$\sqrt{ 6 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$ $ Add the exponent as the base is the same $ $
$\sqrt{ 6 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$\sqrt{ 6 } - \left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$ $ Add $ 1 $ and $ 1$
$\sqrt{ 6 } - \left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$\sqrt{ 6 } - \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$ $ If you square the radical sign, it will disappear $ $
$\sqrt{ 6 } - \color{#FF6800}{ 2 } - \sqrt{ 3 } \left ( \sqrt{ 3 } + \sqrt{ 2 } \right )$
$\sqrt{ 6 } - 2 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$ $ Multiply each term in parentheses by $ - \sqrt{ 3 }$
$\sqrt{ 6 } - 2 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } }$
$\sqrt{ 6 } - 2 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ 3 } - \sqrt{ 3 } \sqrt{ 2 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\sqrt{ 6 } - 2 \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 } - \sqrt{ 3 } \sqrt{ 2 }$
$\sqrt{ 6 } - 2 - \left ( \sqrt{ 3 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 3 } } - \sqrt{ 3 } \sqrt{ 2 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\sqrt{ 6 } - 2 - \left ( \sqrt{ 3 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } - \sqrt{ 3 } \sqrt{ 2 }$
$\sqrt{ 6 } - 2 \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } - \sqrt{ 3 } \sqrt{ 2 }$
$ $ Add the exponent as the base is the same $ $
$\sqrt{ 6 } - 2 \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } - \sqrt{ 3 } \sqrt{ 2 }$
$\sqrt{ 6 } - 2 - \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } - \sqrt{ 3 } \sqrt{ 2 }$
$ $ Add $ 1 $ and $ 1$
$\sqrt{ 6 } - 2 - \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } - \sqrt{ 3 } \sqrt{ 2 }$
$\sqrt{ 6 } - 2 - \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } - \sqrt{ 3 } \sqrt{ 2 }$
$ $ If you square the radical sign, it will disappear $ $
$\sqrt{ 6 } - 2 - \color{#FF6800}{ 3 } - \sqrt{ 3 } \sqrt{ 2 }$
$\sqrt{ 6 } - 2 - 3 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Calculate multiplication $ $
$\sqrt{ 6 } - 2 - 3 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } }$
$\sqrt{ \color{#FF6800}{ 6 } } - 2 - 3 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$- 2 - 3$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Find the sum of the negative numbers $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 5 }$
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