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Calculate the value
Answer
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$\dfrac{ 3 }{ 2 \sqrt{ 3 } } \left( \sqrt{ 2 } - \sqrt{ 3 } \right) - \dfrac{ 2 \sqrt{ 3 } - \sqrt{ 8 } }{ \sqrt{ 2 } }$
$\dfrac { - \sqrt{ 6 } + 1 } { 2 }$
Calculate the value
$\color{#FF6800}{ \dfrac { 3 } { 2 \sqrt{ 3 } } } \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Calculate the expression $ $
$\color{#FF6800}{ \dfrac { 3 \sqrt{ 3 } } { 6 } } \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\color{#FF6800}{ \dfrac { 3 \sqrt{ 3 } } { 6 } } \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Reduce the fraction $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Multiply each term in parentheses by $ \dfrac { \sqrt{ 3 } } { 2 }$
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Arrange the terms multiplied by fractions $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 3 } \sqrt{ 2 } } { 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } } { 2 } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Calculate multiplication of root $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } } { 2 } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( - \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } + \dfrac { \sqrt{ 3 } } { 2 } \times \left ( \color{#FF6800}{ - } \sqrt{ 3 } \right ) - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Move the (-) sign forward $ $
$\dfrac { \sqrt{ 6 } } { 2 } \color{#FF6800}{ - } \dfrac { \sqrt{ 3 } } { 2 } \sqrt{ 3 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \sqrt{ \color{#FF6800}{ 3 } } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Arrange the terms multiplied by fractions $ $
$\dfrac { \sqrt{ 6 } } { 2 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \sqrt{ 3 } \sqrt{ 3 } } { 2 } } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ 3 } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ 3 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 3 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ 3 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Add the exponent as the base is the same $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ Add $ 1 $ and $ 1$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$ $ If you square the radical sign, it will disappear $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { \color{#FF6800}{ 3 } } { 2 } - \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } }$
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { 3 } { 2 } - \color{#FF6800}{ \dfrac { 2 \sqrt{ 3 } - \sqrt{ 8 } } { \sqrt{ 2 } } }$
$ $ Calculate the expression $ $
$\dfrac { \sqrt{ 6 } } { 2 } - \dfrac { 3 } { 2 } - \color{#FF6800}{ \dfrac { 2 \sqrt{ 6 } - \left ( 2 \sqrt{ 2 } \right ) \sqrt{ 2 } } { 2 } }$
$\color{#FF6800}{ \dfrac { \sqrt{ 6 } } { 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 \sqrt{ 6 } - \left ( 2 \sqrt{ 2 } \right ) \sqrt{ 2 } } { 2 } }$
$ $ Combine the fraction with the same denominator $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 2 }$
$\dfrac { \sqrt{ 6 } - 3 - \left ( 2 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 2 }$
$ $ Simplify the expression $ $
$\dfrac { \sqrt{ 6 } - 3 - \left ( 2 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) } { 2 }$
$\dfrac { \sqrt{ 6 } - 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) } { 2 }$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$\dfrac { \sqrt{ 6 } - 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } + \color{#FF6800}{ 4 } } { 2 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } - 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } + 4 } { 2 }$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 6 } } - 3 + 4 } { 2 }$
$\dfrac { - 1 \sqrt{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } } { 2 }$
$ $ Add $ - 3 $ and $ 4$
$\dfrac { - 1 \sqrt{ 6 } + \color{#FF6800}{ 1 } } { 2 }$
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } \sqrt{ 6 } + 1 } { 2 }$
$ $ Multiplying any number by 1 does not change the value $ $
$\dfrac { - \sqrt{ 6 } + 1 } { 2 }$
Solution search results
search-thumbnail-$8 \times $ 
$ = $ In $ \dfrac { E } { 8 } $ $ \left. \begin{array} { l } { \dfrac { 1 } { 3 } } \\ { \dfrac { 11 } { 3 } } \end{array} \right. $ $ \left. \begin{array} { l } { \dfrac { 1 } { 1 } } \\ { \dfrac { 1 } { 1 } } \end{array} \right. $ and $ \left. \begin{array} { l } { δ } \\ { 8 } \end{array} \right. $ 
Find the length of PR. $ \bar { I } $ 
$0$ 
$ \bar { u } $ 
$2$ $ = $ $ \| = $
7th-9th grade
Other
search-thumbnail-Which of the following rational numbers are 
equivalent? 
$0Ptionsy$ 
A \frac{5}{6}, \frac{30}{36} 
B $s\sqrt{rac\left(} -2\right)\left(3\right)\sqrt{1rac} \sqrt{4\right)16\right)4} $ 
C $s\sqrt{11aC\left(} -4\right)1-7b,\sqrt{1rac\left(16\sqrt{35\right)9} } $ 
D \frac{1}{2},\frac{3}{8}
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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