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Answer
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$\dfrac{ \sqrt{ 27 } +3 }{ \sqrt{ 3 } } - \dfrac{ \sqrt{ 8 } - \sqrt{ 6 } }{ \sqrt{ 2 } }$
$1 + 2 \sqrt{ 3 }$
Calculate the value
$\color{#FF6800}{ \dfrac { \sqrt{ 27 } + 3 } { \sqrt{ 3 } } } - \dfrac { \sqrt{ 8 } - \sqrt{ 6 } } { \sqrt{ 2 } }$
$ $ Calculate the expression $ $
$\color{#FF6800}{ \dfrac { 9 + 3 \sqrt{ 3 } } { 3 } } - \dfrac { \sqrt{ 8 } - \sqrt{ 6 } } { \sqrt{ 2 } }$
$\color{#FF6800}{ \dfrac { 9 + 3 \sqrt{ 3 } } { 3 } } - \dfrac { \sqrt{ 8 } - \sqrt{ 6 } } { \sqrt{ 2 } }$
$ $ Reduce the fraction $ $
$\color{#FF6800}{ 3 } + \sqrt{ \color{#FF6800}{ 3 } } - \dfrac { \sqrt{ 8 } - \sqrt{ 6 } } { \sqrt{ 2 } }$
$3 + \sqrt{ 3 } - \color{#FF6800}{ \dfrac { \sqrt{ 8 } - \sqrt{ 6 } } { \sqrt{ 2 } } }$
$ $ Calculate the expression $ $
$3 + \sqrt{ 3 } - \color{#FF6800}{ \dfrac { 4 - \left ( 2 \sqrt{ 3 } \right ) } { 2 } }$
$3 + \sqrt{ 3 } - \dfrac { 4 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { 2 }$
$ $ Get rid of unnecessary parentheses $ $
$3 + \sqrt{ 3 } - \dfrac { 4 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } } { 2 }$
$3 + \sqrt{ 3 } - \color{#FF6800}{ \dfrac { 4 - 2 \sqrt{ 3 } } { 2 } }$
$ $ Reduce the fraction $ $
$3 + \sqrt{ 3 } - \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$3 + \sqrt{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$3 + \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } + \sqrt{ \color{#FF6800}{ 3 } }$
$\color{#FF6800}{ 3 } + \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } + \sqrt{ 3 }$
$ $ Subtract $ 2 $ from $ 3$
$\color{#FF6800}{ 1 } + \sqrt{ 3 } + \sqrt{ 3 }$
$1 + \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } }$
$ $ Calculate between similar terms $ $
$1 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } }$
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