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Formula
Calculate the value
$\sqrt{ \left( 5-2 \sqrt{ 6 } \right) ^{ 2 } + \left( 5+2 \sqrt{ 6 } \right) ^{ 2 } }$
$7 \sqrt{ 2 }$
Calculate the value
$\sqrt{ \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 2 } } + \left ( 5 + 2 \sqrt{ 6 } \right ) ^ { 2 } }$
 Calculate power 
$\sqrt{ \color{#FF6800}{ 49 } \color{#FF6800}{ - } \color{#FF6800}{ 20 } \sqrt{ \color{#FF6800}{ 6 } } + \left ( 5 + 2 \sqrt{ 6 } \right ) ^ { 2 } }$
$\sqrt{ 49 - 20 \sqrt{ 6 } + \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
 Calculate power 
$\sqrt{ 49 - 20 \sqrt{ 6 } + \color{#FF6800}{ 20 } \sqrt{ \color{#FF6800}{ 6 } } + \color{#FF6800}{ 49 } }$
$\sqrt{ 49 \color{#FF6800}{ - } \color{#FF6800}{ 20 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 20 } \sqrt{ \color{#FF6800}{ 6 } } + 49 }$
 Eliminate opponent number 
$\sqrt{ 49 + 49 }$
$\sqrt{ \color{#FF6800}{ 49 } \color{#FF6800}{ + } \color{#FF6800}{ 49 } }$
 Add $49$ and $49$
$\sqrt{ \color{#FF6800}{ 98 } }$
$\sqrt{ \color{#FF6800}{ 98 } }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$\color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 2 } }$
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