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$\left( 1- \sqrt{ 6 } \right) \left( -1- \sqrt{ 6 } \right)$
$5$
Calculate the value
$\left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right )$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\color{#FF6800}{ 1 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right ) \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right )$
$\color{#FF6800}{ 1 } \times \left ( - 1 \right ) + 1 \times \left ( - \sqrt{ 6 } \right ) - \sqrt{ 6 } \times \left ( - 1 \right ) - \sqrt{ 6 } \times \left ( - \sqrt{ 6 } \right )$
$ $ Multiplying any number by 1 does not change the value $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } + 1 \times \left ( - \sqrt{ 6 } \right ) - \sqrt{ 6 } \times \left ( - 1 \right ) - \sqrt{ 6 } \times \left ( - \sqrt{ 6 } \right )$
$- 1 + \color{#FF6800}{ 1 } \times \left ( - \sqrt{ 6 } \right ) - \sqrt{ 6 } \times \left ( - 1 \right ) - \sqrt{ 6 } \times \left ( - \sqrt{ 6 } \right )$
$ $ Multiplying any number by 1 does not change the value $ $
$- 1 - \sqrt{ 6 } - \sqrt{ 6 } \times \left ( - 1 \right ) - \sqrt{ 6 } \times \left ( - \sqrt{ 6 } \right )$
$- 1 - \sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) - \sqrt{ 6 } \times \left ( - \sqrt{ 6 } \right )$
$ $ Simplify the expression $ $
$- 1 - \sqrt{ 6 } + \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 6 } } - \sqrt{ 6 } \times \left ( - \sqrt{ 6 } \right )$
$- 1 - \sqrt{ 6 } + \color{#FF6800}{ 1 } \sqrt{ 6 } - \sqrt{ 6 } \times \left ( - \sqrt{ 6 } \right )$
$ $ Multiplying any number by 1 does not change the value $ $
$- 1 - \sqrt{ 6 } + \sqrt{ 6 } - \sqrt{ 6 } \times \left ( - \sqrt{ 6 } \right )$
$- 1 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } } - \sqrt{ 6 } \times \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right )$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$- 1 - \sqrt{ 6 } \times \left ( - \sqrt{ 6 } \right )$
$- 1 \color{#FF6800}{ - } \sqrt{ 6 } \times \left ( \color{#FF6800}{ - } \sqrt{ 6 } \right )$
$ $ Since negative numbers are multiplied by an even number, remove the (-) sign $ $
$- 1 + \sqrt{ 6 } \sqrt{ 6 }$
$- 1 + \sqrt{ \color{#FF6800}{ 6 } } \sqrt{ 6 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$- 1 + \left ( \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 6 }$
$- 1 + \left ( \sqrt{ 6 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 6 } }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$- 1 + \left ( \sqrt{ 6 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 1 } }$
$- 1 + \left ( \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 1 } }$
$ $ Add the exponent as the base is the same $ $
$- 1 + \left ( \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$- 1 + \left ( \sqrt{ 6 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$ $ Add $ 1 $ and $ 1$
$- 1 + \left ( \sqrt{ 6 } \right ) ^ { \color{#FF6800}{ 2 } }$
$- 1 + \left ( \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ If you square the radical sign, it will disappear $ $
$- 1 + \color{#FF6800}{ 6 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$ $ Add $ - 1 $ and $ 6$
$\color{#FF6800}{ 5 }$
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