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$3 \sqrt{ 2 } + 2$
Calculate the value
$\color{#FF6800}{ \dfrac { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } } { \sqrt{ \color{#FF6800}{ 2 } } } } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$ $ Calculate the expression $ $
$\color{#FF6800}{ \dfrac { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 2 } } } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$\dfrac { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } \sqrt{ 2 } } { 2 } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$ $ Calculate power $ $
$\dfrac { \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \right ) \sqrt{ 2 } } { 2 } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$\color{#FF6800}{ \dfrac { \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \right ) \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 2 } } } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$ $ Reduce the fraction $ $
$\left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \sqrt{ \color{#FF6800}{ 2 } } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$\left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \sqrt{ \color{#FF6800}{ 2 } } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$ $ Multiply each term in parentheses by $ \sqrt{ 2 }$
$\left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$\left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } + 3 \sqrt{ 2 } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$ $ Get rid of unnecessary parentheses $ $
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + 3 \sqrt{ 2 } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + 3 \sqrt{ 2 } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 4 } + 3 \sqrt{ 2 } + \left ( \sqrt{ 2 } + 2 \right ) \left ( \sqrt{ 2 } - 2 \right )$
$4 + 3 \sqrt{ 2 } + \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$4 + 3 \sqrt{ 2 } + \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } }$
$4 + 3 \sqrt{ 2 } + \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } - 2 ^ { 2 }$
$ $ If you square the radical sign, it will disappear $ $
$4 + 3 \sqrt{ 2 } + \color{#FF6800}{ 2 } - 2 ^ { 2 }$
$4 + 3 \sqrt{ 2 } + 2 - \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } }$
$ $ Calculate power $ $
$4 + 3 \sqrt{ 2 } + 2 - \color{#FF6800}{ 4 }$
$\color{#FF6800}{ 4 } + 3 \sqrt{ 2 } + 2 \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$3 \sqrt{ 2 } + 2$
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