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$\dfrac { 30 \sqrt{ 2 } + \sqrt{ 5 } } { 5 }$
Calculate the value
$8 \sqrt{ 2 } + \sqrt{ \color{#FF6800}{ 45 } } - \dfrac { 12 } { \sqrt{ 18 } } - \dfrac { 14 } { \sqrt{ 5 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$8 \sqrt{ 2 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } - \dfrac { 12 } { \sqrt{ 18 } } - \dfrac { 14 } { \sqrt{ 5 } }$
$8 \sqrt{ 2 } + 3 \sqrt{ 5 } - \color{#FF6800}{ \dfrac { \color{#FF6800}{ 12 } } { \sqrt{ \color{#FF6800}{ 18 } } } } - \dfrac { 14 } { \sqrt{ 5 } }$
$ $ Calculate the expression $ $
$8 \sqrt{ 2 } + 3 \sqrt{ 5 } - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) - \dfrac { 14 } { \sqrt{ 5 } }$
$8 \sqrt{ 2 } + 3 \sqrt{ 5 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) - \dfrac { 14 } { \sqrt{ 5 } }$
$ $ Get rid of unnecessary parentheses $ $
$8 \sqrt{ 2 } + 3 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } - \dfrac { 14 } { \sqrt{ 5 } }$
$8 \sqrt{ 2 } + 3 \sqrt{ 5 } - 2 \sqrt{ 2 } - \color{#FF6800}{ \dfrac { \color{#FF6800}{ 14 } } { \sqrt{ \color{#FF6800}{ 5 } } } }$
$ $ Calculate the expression $ $
$8 \sqrt{ 2 } + 3 \sqrt{ 5 } - 2 \sqrt{ 2 } - \color{#FF6800}{ \dfrac { \color{#FF6800}{ 14 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } }$
$\color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 2 } } + 3 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } - \dfrac { 14 \sqrt{ 5 } } { 5 }$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + 3 \sqrt{ 5 } - \dfrac { 14 \sqrt{ 5 } } { 5 }$
$6 \sqrt{ 2 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } - \dfrac { 14 \sqrt{ 5 } } { 5 }$
$ $ Convert an equation to a fraction using $ a=\dfrac{a}{1}$
$6 \sqrt{ 2 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 1 } } } - \dfrac { 14 \sqrt{ 5 } } { 5 }$
$6 \sqrt{ 2 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 1 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 14 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } }$
$ $ Write all numerators above the least common denominator $ $
$6 \sqrt{ 2 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 15 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 14 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } }$
$6 \sqrt{ 2 } + \dfrac { \color{#FF6800}{ 15 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 14 } \sqrt{ \color{#FF6800}{ 5 } } } { 5 }$
$ $ Calculate between similar terms $ $
$6 \sqrt{ 2 } + \dfrac { \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 5 } } } { 5 }$
$6 \sqrt{ 2 } + \dfrac { \color{#FF6800}{ 1 } \sqrt{ 5 } } { 5 }$
$ $ Multiplying any number by 1 does not change the value $ $
$6 \sqrt{ 2 } + \dfrac { \sqrt{ 5 } } { 5 }$
$\color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } }$
$ $ Find the sum of the fractions $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 30 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } }$
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