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Calculate the value
Answer
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$\sqrt{ 24 } + \left( \sqrt{ 12 } + \sqrt{ 3 } \right) \div \dfrac{ 1 }{ \sqrt{ 2 } }$
$5 \sqrt{ 6 }$
Calculate the value
$\sqrt{ \color{#FF6800}{ 24 } } + \left ( \sqrt{ 12 } + \sqrt{ 3 } \right ) \div \dfrac { 1 } { \sqrt{ 2 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } + \left ( \sqrt{ 12 } + \sqrt{ 3 } \right ) \div \dfrac { 1 } { \sqrt{ 2 } }$
$2 \sqrt{ 6 } + \left ( \sqrt{ \color{#FF6800}{ 12 } } + \sqrt{ 3 } \right ) \div \dfrac { 1 } { \sqrt{ 2 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$2 \sqrt{ 6 } + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 3 } \right ) \div \dfrac { 1 } { \sqrt{ 2 } }$
$2 \sqrt{ 6 } + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right ) \div \dfrac { 1 } { \sqrt{ 2 } }$
$ $ Calculate between similar terms $ $
$2 \sqrt{ 6 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \div \dfrac { 1 } { \sqrt{ 2 } }$
$2 \sqrt{ 6 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \div } \color{#FF6800}{ \dfrac { 1 } { \sqrt{ 2 } } }$
$ $ Arrange the terms multiplied by fractions $ $
$2 \sqrt{ 6 } + \color{#FF6800}{ \dfrac { 3 \sqrt{ 3 } \sqrt{ 2 } } { 1 } }$
$2 \sqrt{ 6 } + \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } } { 1 }$
$ $ Simplify the expression $ $
$2 \sqrt{ 6 } + \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } } } { 1 }$
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } + \dfrac { 3 \sqrt{ 6 } } { 1 }$
$ $ Convert an equation to a fraction using $ a=\dfrac{a}{1}$
$\color{#FF6800}{ \dfrac { 2 \sqrt{ 6 } } { 1 } } + \dfrac { 3 \sqrt{ 6 } } { 1 }$
$\color{#FF6800}{ \dfrac { 2 \sqrt{ 6 } } { 1 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 \sqrt{ 6 } } { 1 } }$
$ $ Since the denominator is the same as $ 1 $ , combine the fractions into one $ $
$\color{#FF6800}{ \dfrac { 2 \sqrt{ 6 } + 3 \sqrt{ 6 } } { 1 } }$
$\dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } } } { 1 }$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 6 } } } { 1 }$
$\dfrac { 5 \sqrt{ 6 } } { \color{#FF6800}{ 1 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$\color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 6 } }$
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