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$\left( 7 \sqrt{ 5 } + \sqrt{ 2 } \right) \left( \sqrt{ 5 } -3 \sqrt{ 2 } \right)$
$29 - 20 \sqrt{ 10 }$
Calculate the value
$\left ( \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\left ( \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$\left ( \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \sqrt{ \color{#FF6800}{ 5 } } + \left ( 7 \sqrt{ 5 } \right ) \times \left ( - 3 \sqrt{ 2 } \right ) + \sqrt{ 2 } \sqrt{ 5 } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } } + \left ( 7 \sqrt{ 5 } \right ) \times \left ( - 3 \sqrt{ 2 } \right ) + \sqrt{ 2 } \sqrt{ 5 } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$\color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } } + \left ( 7 \sqrt{ 5 } \right ) \times \left ( - 3 \sqrt{ 2 } \right ) + \sqrt{ 2 } \sqrt{ 5 } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 35 } + \left ( 7 \sqrt{ 5 } \right ) \times \left ( - 3 \sqrt{ 2 } \right ) + \sqrt{ 2 } \sqrt{ 5 } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$35 + \left ( \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ 2 } \sqrt{ 5 } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$35 \color{#FF6800}{ - } \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \sqrt{ 5 } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$35 \color{#FF6800}{ - } \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \sqrt{ 5 } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$ $ Simplify the expression $ $
$35 \color{#FF6800}{ - } \color{#FF6800}{ 21 } \sqrt{ \color{#FF6800}{ 10 } } + \sqrt{ 2 } \sqrt{ 5 } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$35 - 21 \sqrt{ 10 } + \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 5 } } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$ $ Calculate multiplication of root $ $
$35 - 21 \sqrt{ 10 } + \sqrt{ \color{#FF6800}{ 10 } } + \sqrt{ 2 } \times \left ( - 3 \sqrt{ 2 } \right )$
$35 - 21 \sqrt{ 10 } + \sqrt{ 10 } + \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$ $ Get rid of unnecessary parentheses $ $
$35 - 21 \sqrt{ 10 } + \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } }$
$35 - 21 \sqrt{ 10 } + \sqrt{ 10 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Simplify the expression $ $
$35 - 21 \sqrt{ 10 } + \sqrt{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ 35 } - 21 \sqrt{ 10 } + \sqrt{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ Subtract $ 6 $ from $ 35$
$\color{#FF6800}{ 29 } - 21 \sqrt{ 10 } + \sqrt{ 10 }$
$29 \color{#FF6800}{ - } \color{#FF6800}{ 21 } \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 10 } }$
$ $ Calculate between similar terms $ $
$29 \color{#FF6800}{ - } \color{#FF6800}{ 20 } \sqrt{ \color{#FF6800}{ 10 } }$
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