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Formula
Calculate the value
$\sqrt{ 2 } \left( \sqrt{ 2 } - \sqrt{ 3 } \right) + \sqrt{ 3 } \left( \sqrt{ 2 } + \sqrt{ 3 } \right)$
$5$
Calculate the value
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
 Multiply each term in parentheses by $\sqrt{ 2 }$
$\sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\sqrt{ \color{#FF6800}{ 2 } } \sqrt{ 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
 If the exponent is omitted, the exponent of that term is equal to 1 
$\left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\left ( \sqrt{ 2 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
 If the exponent is omitted, the exponent of that term is equal to 1 
$\left ( \sqrt{ 2 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
 Add the exponent as the base is the same 
$\left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
 Add $1$ and $1$
$\left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
 If you square the radical sign, it will disappear 
$\color{#FF6800}{ 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$2 + \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
 Move the (-) sign forward 
$2 \color{#FF6800}{ - } \sqrt{ 2 } \sqrt{ 3 } + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$2 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
 Calculate multiplication 
$2 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$2 - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 3 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right )$
 Multiply each term in parentheses by $\sqrt{ 3 }$
$2 - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 3 } }$
$2 - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 3 } \sqrt{ 3 }$
 Calculate multiplication of root 
$2 - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 3 } \sqrt{ 3 }$
$2 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 3 } \sqrt{ 3 }$
 Remove the two numbers if the values are the same and the signs are different 
$2 + \sqrt{ 3 } \sqrt{ 3 }$
$2 + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ 3 }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$2 + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 }$
$2 + \left ( \sqrt{ 3 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 3 } }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$2 + \left ( \sqrt{ 3 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } }$
$2 + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } }$
 Add the exponent as the base is the same 
$2 + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$2 + \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
 Add $1$ and $1$
$2 + \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 2 } }$
$2 + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } }$
 If you square the radical sign, it will disappear 
$2 + \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
 Add $2$ and $3$
$\color{#FF6800}{ 5 }$
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