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$- 12 + 5 \sqrt{ 6 }$
Calculate the value
$\sqrt{ \left ( 2 - \sqrt{ 6 } \right ) ^ { \color{#FF6800}{ 2 } } } - \sqrt{ \left ( 4 \sqrt{ 6 } - 10 \right ) ^ { 2 } }$
$ $ Organize as the power is written in the radical sign, and the root exponent and the exponent are the same $ $
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right ) - \sqrt{ \left ( 4 \sqrt{ 6 } - 10 \right ) ^ { 2 } }$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right ) - \sqrt{ \left ( 4 \sqrt{ 6 } - 10 \right ) ^ { 2 } }$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } + \sqrt{ \color{#FF6800}{ 6 } } - \sqrt{ \left ( 4 \sqrt{ 6 } - 10 \right ) ^ { 2 } }$
$- 2 + \sqrt{ 6 } - \sqrt{ \left ( 4 \sqrt{ 6 } - 10 \right ) ^ { \color{#FF6800}{ 2 } } }$
$ $ Organize as the power is written in the radical sign, and the root exponent and the exponent are the same $ $
$- 2 + \sqrt{ 6 } - \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } \right ) \right )$
$- 2 + \sqrt{ 6 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \left ( 4 \sqrt{ 6 } - 10 \right ) \right )$
$ $ Simplify Minus $ $
$- 2 + \sqrt{ 6 } + 4 \sqrt{ 6 } - 10$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } + \sqrt{ 6 } + 4 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 10 }$
$ $ Find the sum of the negative numbers $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 12 } + \sqrt{ 6 } + 4 \sqrt{ 6 }$
$- 12 + \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 6 } }$
$ $ Calculate between similar terms $ $
$- 12 + \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 6 } }$
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