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Answer
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$\left( 5 \sqrt{ 3 } + \sqrt{ 2 } \right) \left( 4 \sqrt{ 3 } - \sqrt{ 2 } \right)$
$58 - \sqrt{ 6 }$
Calculate the value
$\left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$\left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \left ( 5 \sqrt{ 3 } \right ) \times \left ( - \sqrt{ 2 } \right ) + \sqrt{ 2 } \left ( 4 \sqrt{ 3 } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$\color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } + \left ( 5 \sqrt{ 3 } \right ) \times \left ( - \sqrt{ 2 } \right ) + \sqrt{ 2 } \left ( 4 \sqrt{ 3 } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$\color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } + \left ( 5 \sqrt{ 3 } \right ) \times \left ( - \sqrt{ 2 } \right ) + \sqrt{ 2 } \left ( 4 \sqrt{ 3 } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 60 } + \left ( 5 \sqrt{ 3 } \right ) \times \left ( - \sqrt{ 2 } \right ) + \sqrt{ 2 } \left ( 4 \sqrt{ 3 } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$60 + \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ 2 } \left ( 4 \sqrt{ 3 } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$60 + \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ 2 } \left ( 4 \sqrt{ 3 } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$60 + \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \sqrt{ 2 } \left ( 4 \sqrt{ 3 } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$ $ Simplify the expression $ $
$60 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 2 } \left ( 4 \sqrt{ 3 } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$60 - 5 \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$60 - 5 \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$60 - 5 \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$ $ Simplify the expression $ $
$60 - 5 \sqrt{ 6 } + \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 2 } \right )$
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } + \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \sqrt{ 2 } \right )$
$ $ Move the (-) sign forward $ $
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ 2 } \sqrt{ 2 }$
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ 2 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 2 }$
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } - \left ( \sqrt{ 2 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } - \left ( \sqrt{ 2 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } }$
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } }$
$ $ Add the exponent as the base is the same $ $
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } - \left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$ $ Add $ 1 $ and $ 1$
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } - \left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 2 } }$
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } - \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ If you square the radical sign, it will disappear $ $
$60 - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } - \color{#FF6800}{ 2 }$
$\color{#FF6800}{ 60 } - 5 \sqrt{ 6 } + 4 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$ $ Subtract $ 2 $ from $ 60$
$\color{#FF6800}{ 58 } - 5 \sqrt{ 6 } + 4 \sqrt{ 6 }$
$58 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 6 } }$
$ $ Calculate between similar terms $ $
$58 \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 6 } }$
$58 \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ 6 }$
$ $ Multiplying any number by 1 does not change the value $ $
$58 - \sqrt{ 6 }$
Solution search results
search-thumbnail-$s|ef\left(-1n$ $\left($ }\right)^{50}\ $\right)$ \ | | is\ equal\ to\ $S$ 
$s1S$ 
$S-1S$ 
$s2S$ 
$s50s$
7th-9th grade
Other
search-thumbnail-The rationalizing factor of \sqrt{23} is 
$°$ $Options^{°}$ $0$ 
A 24 
23 
C \sqrt{23} 
D None of these
7th-9th grade
Other
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