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Calculate the value

Answer

$\dfrac { - \sqrt{ 6 } + 3 \sqrt{ 7 } } { 9 }$

Calculate the value

$\dfrac { \sqrt{ 6 } } { 9 } - \dfrac { \sqrt{ \color{#FF6800}{ 24 } } } { 9 } + \dfrac { \sqrt{ 7 } } { 3 }$

$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $

$\dfrac { \sqrt{ 6 } } { 9 } - \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } } { 9 } + \dfrac { \sqrt{ 7 } } { 3 }$

$\color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 9 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 9 } } } + \dfrac { \sqrt{ 7 } } { 3 }$

$ $ Since the denominator is the same as $ 9 $ , combine the fractions into one $ $

$\color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) } { \color{#FF6800}{ 9 } } } + \dfrac { \sqrt{ 7 } } { 3 }$

$\dfrac { \sqrt{ 6 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) } { 9 } + \dfrac { \sqrt{ 7 } } { 3 }$

$ $ Get rid of unnecessary parentheses $ $

$\dfrac { \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } } { 9 } + \dfrac { \sqrt{ 7 } } { 3 }$

$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } } { 9 } + \dfrac { \sqrt{ 7 } } { 3 }$

$ $ Calculate between similar terms $ $

$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 6 } } } { 9 } + \dfrac { \sqrt{ 7 } } { 3 }$

$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ 6 } } { 9 } + \dfrac { \sqrt{ 7 } } { 3 }$

$ $ Multiplying any number by 1 does not change the value $ $

$\dfrac { - \sqrt{ 6 } } { 9 } + \dfrac { \sqrt{ 7 } } { 3 }$

$\dfrac { \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } } { 9 } + \dfrac { \sqrt{ 7 } } { 3 }$

$ $ Move the minus sign to the front of the fraction $ $

$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 9 } } } + \dfrac { \sqrt{ 7 } } { 3 }$

$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 6 } } } { \color{#FF6800}{ 9 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 7 } } } { \color{#FF6800}{ 3 } } }$

$ $ Find the sum of the fractions $ $

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 7 } } } { \color{#FF6800}{ 9 } } }$

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