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$5 \sqrt{ 5 } - 6 \sqrt{ 2 }$
Calculate the value
$\sqrt{ \color{#FF6800}{ 45 } } - \sqrt{ 8 } + \sqrt{ 20 } - \sqrt{ 32 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } - \sqrt{ 8 } + \sqrt{ 20 } - \sqrt{ 32 }$
$3 \sqrt{ 5 } - \sqrt{ \color{#FF6800}{ 8 } } + \sqrt{ 20 } - \sqrt{ 32 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$3 \sqrt{ 5 } - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ 20 } - \sqrt{ 32 }$
$3 \sqrt{ 5 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ 20 } - \sqrt{ 32 }$
$ $ Get rid of unnecessary parentheses $ $
$3 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 20 } - \sqrt{ 32 }$
$3 \sqrt{ 5 } - 2 \sqrt{ 2 } + \sqrt{ \color{#FF6800}{ 20 } } - \sqrt{ 32 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$3 \sqrt{ 5 } - 2 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } - \sqrt{ 32 }$
$3 \sqrt{ 5 } - 2 \sqrt{ 2 } + 2 \sqrt{ 5 } - \sqrt{ \color{#FF6800}{ 32 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$3 \sqrt{ 5 } - 2 \sqrt{ 2 } + 2 \sqrt{ 5 } - \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$3 \sqrt{ 5 } - 2 \sqrt{ 2 } + 2 \sqrt{ 5 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$ $ Get rid of unnecessary parentheses $ $
$3 \sqrt{ 5 } - 2 \sqrt{ 2 } + 2 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } - 2 \sqrt{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } - 4 \sqrt{ 2 }$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 5 } } - 2 \sqrt{ 2 } - 4 \sqrt{ 2 }$
$5 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Calculate between similar terms $ $
$5 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } }$
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