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Answer
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$\sqrt{ 5 } \left( \sqrt{ 12 } - \sqrt{ 45 } \right)$
$2 \sqrt{ 15 } - 15$
Calculate the value
$\sqrt{ 5 } \left ( \sqrt{ \color{#FF6800}{ 12 } } - \sqrt{ 45 } \right )$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\sqrt{ 5 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } - \sqrt{ 45 } \right )$
$\sqrt{ 5 } \left ( 2 \sqrt{ 3 } - \sqrt{ \color{#FF6800}{ 45 } } \right )$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\sqrt{ 5 } \left ( 2 \sqrt{ 3 } - \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \right )$
$\sqrt{ 5 } \left ( 2 \sqrt{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \right )$
$ $ Get rid of unnecessary parentheses $ $
$\sqrt{ 5 } \left ( 2 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right )$
$\sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right )$
$ $ Multiply each term in parentheses by $ \sqrt{ 5 }$
$\sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right )$
$\sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \sqrt{ 5 } \times \left ( - 3 \sqrt{ 5 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 5 } \times \left ( - 3 \sqrt{ 5 } \right )$
$\sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 5 } \times \left ( - 3 \sqrt{ 5 } \right )$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 15 } } + \sqrt{ 5 } \times \left ( - 3 \sqrt{ 5 } \right )$
$2 \sqrt{ 15 } + \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right )$
$ $ Get rid of unnecessary parentheses $ $
$2 \sqrt{ 15 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } }$
$2 \sqrt{ 15 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } }$
$ $ Simplify the expression $ $
$2 \sqrt{ 15 } \color{#FF6800}{ - } \color{#FF6800}{ 15 }$
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