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Answer
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$\dfrac { 5 \sqrt{ 2 } } { 6 }$
Calculate the value
$\color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 3 } } }$
$ $ Write all numerators above the least common denominator $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 6 } } }$
$\dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 6 }$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } } { 6 }$
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