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Calculate the value
Answer
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$\sqrt{ 27 } \left( \sqrt{ 6 } - \dfrac{ 2 }{ \sqrt{ 3 } } \right) -3 \left( \sqrt{ 8 } -1 \right)$
$3 \sqrt{ 2 } - 3$
Calculate the value
$\sqrt{ \color{#FF6800}{ 27 } } \left ( \sqrt{ 6 } - \dfrac { 2 } { \sqrt{ 3 } } \right ) - 3 \left ( \sqrt{ 8 } - 1 \right )$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \left ( \sqrt{ 6 } - \dfrac { 2 } { \sqrt{ 3 } } \right ) - 3 \left ( \sqrt{ 8 } - 1 \right )$
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } } \left ( \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { \sqrt{ 3 } } } \right ) - 3 \left ( \sqrt{ 8 } - 1 \right )$
$ $ Expand the expression to calculate the value $ $
$\color{#FF6800}{ 9 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } - 3 \left ( \sqrt{ 8 } - 1 \right )$
$9 \sqrt{ 2 } - 6 - 3 \left ( \sqrt{ \color{#FF6800}{ 8 } } - 1 \right )$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$9 \sqrt{ 2 } - 6 - 3 \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } - 1 \right )$
$9 \sqrt{ 2 } - 6 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$ $ Multiply each term in parentheses by $ - 3$
$9 \sqrt{ 2 } - 6 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \color{#FF6800}{ 3 }$
$9 \sqrt{ 2 } - 6 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + 3$
$ $ Get rid of unnecessary parentheses $ $
$9 \sqrt{ 2 } - 6 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + 3$
$9 \sqrt{ 2 } - 6 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + 3$
$ $ Simplify the expression $ $
$9 \sqrt{ 2 } - 6 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + 3$
$\color{#FF6800}{ 9 } \sqrt{ \color{#FF6800}{ 2 } } - 6 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + 3$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } - 6 + 3$
$3 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$ $ Add $ - 6 $ and $ 3$
$3 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
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