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$- 5 - \sqrt{ 7 }$
Calculate the value
$\left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right )$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\sqrt{ \color{#FF6800}{ 7 } } \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 7 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right )$
$\sqrt{ \color{#FF6800}{ 7 } } \sqrt{ 7 } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 7 } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$\left ( \sqrt{ 7 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 7 } } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\left ( \sqrt{ 7 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 1 } } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$\left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 1 } } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$ $ Add the exponent as the base is the same $ $
$\left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$\left ( \sqrt{ 7 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$ $ Add $ 1 $ and $ 1$
$\left ( \sqrt{ 7 } \right ) ^ { \color{#FF6800}{ 2 } } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$\left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 2 } } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$ $ If you square the radical sign, it will disappear $ $
$\color{#FF6800}{ 7 } + \sqrt{ 7 } \left ( - 4 \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$7 + \sqrt{ \color{#FF6800}{ 7 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$ $ Simplify the expression $ $
$7 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 7 } } + 3 \sqrt{ 7 } + 3 \times \left ( - 4 \right )$
$7 - 4 \sqrt{ 7 } + 3 \sqrt{ 7 } + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right )$
$ $ Multiply $ 3 $ and $ - 4$
$7 - 4 \sqrt{ 7 } + 3 \sqrt{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 12 }$
$\color{#FF6800}{ 7 } - 4 \sqrt{ 7 } + 3 \sqrt{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 12 }$
$ $ Subtract $ 12 $ from $ 7$
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } - 4 \sqrt{ 7 } + 3 \sqrt{ 7 }$
$- 5 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 7 } }$
$ $ Calculate between similar terms $ $
$- 5 \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 7 } }$
$- 5 \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ 7 }$
$ $ Multiplying any number by 1 does not change the value $ $
$- 5 - \sqrt{ 7 }$
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