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Formula
Calculate the value
$\left( \sqrt{ 18 } -2 \sqrt{ 5 } \right) \sqrt{ 2 } - \sqrt{ 5 } \left( \sqrt{ 8 } + \sqrt{ 5 } \right)$
$1 - 4 \sqrt{ 10 }$
Calculate the value
$\left ( \sqrt{ \color{#FF6800}{ 18 } } - 2 \sqrt{ 5 } \right ) \sqrt{ 2 } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$\left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } - 2 \sqrt{ 5 } \right ) \sqrt{ 2 } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
$\left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
 Multiply each term in parentheses by $\sqrt{ 2 }$
$\left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
$\left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 5 } \right ) \sqrt{ 2 } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
 Get rid of unnecessary parentheses 
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 5 } \right ) \sqrt{ 2 } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 5 } \right ) \sqrt{ 2 } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
 Simplify the expression 
$\color{#FF6800}{ 6 } + \left ( - 2 \sqrt{ 5 } \right ) \sqrt{ 2 } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
$6 + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
 Get rid of unnecessary parentheses 
$6 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
$6 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
 Simplify the expression 
$6 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } } - \sqrt{ 5 } \left ( \sqrt{ 8 } + \sqrt{ 5 } \right )$
$6 - 2 \sqrt{ 10 } - \sqrt{ 5 } \left ( \sqrt{ \color{#FF6800}{ 8 } } + \sqrt{ 5 } \right )$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$6 - 2 \sqrt{ 10 } - \sqrt{ 5 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 5 } \right )$
$6 - 2 \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \right )$
 Multiply each term in parentheses by $- \sqrt{ 5 }$
$6 - 2 \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } }$
$6 - 2 \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) - \sqrt{ 5 } \sqrt{ 5 }$
 Get rid of unnecessary parentheses 
$6 - 2 \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 5 } \sqrt{ 5 }$
$6 - 2 \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 5 } \sqrt{ 5 }$
 Simplify the expression 
$6 - 2 \sqrt{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } } - \sqrt{ 5 } \sqrt{ 5 }$
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ 5 }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 5 }$
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } - \left ( \sqrt{ 5 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 5 } }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } - \left ( \sqrt{ 5 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } }$
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } }$
 Add the exponent as the base is the same 
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } - \left ( \sqrt{ 5 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
 Add $1$ and $1$
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } - \left ( \sqrt{ 5 } \right ) ^ { \color{#FF6800}{ 2 } }$
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } - \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } }$
 If you square the radical sign, it will disappear 
$6 - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } - \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 6 } - 2 \sqrt{ 10 } - 2 \sqrt{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
 Subtract $5$ from $6$
$\color{#FF6800}{ 1 } - 2 \sqrt{ 10 } - 2 \sqrt{ 10 }$
$1 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } }$
 Calculate between similar terms 
$1 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 10 } }$
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