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