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Calculate the value
Answer
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$\dfrac{ \sqrt{ 6 } }{ \sqrt{ 2 } + \sqrt{ 3 } }$
$- 2 \sqrt{ 3 } + 3 \sqrt{ 2 }$
Calculate the value
$\dfrac { \sqrt{ 6 } } { \sqrt{ 2 } + \sqrt{ 3 } }$
$ $ Find the conjugate irrational number of denominator $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 6 } } { \sqrt{ 2 } + \sqrt{ 3 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 2 } - \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } } }$
$\dfrac { \sqrt{ 6 } } { \sqrt{ 2 } + \sqrt{ 3 } } \times \dfrac { \sqrt{ 2 } - \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 6 } \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) } { \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) }$
$ $ Multiply each term in parentheses by $ \sqrt{ 6 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) }$
$\dfrac { \sqrt{ 6 } \sqrt{ 2 } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { \sqrt{ 6 } \sqrt{ 2 } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$ $ Arrange the expression $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$\dfrac { \sqrt{ 6 \times 2 } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 6 \times 2 } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { \color{#FF6800}{ 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$\dfrac { \sqrt{ 6 \times 2 } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 6 \times 2 } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - \color{#FF6800}{ 3 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 }$
$ $ Multiply $ 6 $ and $ 2$
$\dfrac { \sqrt{ \color{#FF6800}{ 12 } } + \sqrt{ 6 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 }$
$\dfrac { \sqrt{ 12 } + \sqrt{ 6 } \times \left ( \color{#FF6800}{ - } \sqrt{ 3 } \right ) } { 2 - 3 }$
$ $ Move the (-) sign forward $ $
$\dfrac { \sqrt{ 12 } \color{#FF6800}{ - } \sqrt{ 6 } \sqrt{ 3 } } { 2 - 3 }$
$\dfrac { \sqrt{ 12 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \sqrt{ \color{#FF6800}{ 3 } } } { 2 - 3 }$
$ $ Calculate multiplication $ $
$\dfrac { \sqrt{ 12 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 2 - 3 }$
$\dfrac { \sqrt{ 12 } - \left ( 3 \sqrt{ 2 } \right ) } { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } }$
$ $ Subtract $ 3 $ from $ 2$
$\dfrac { \sqrt{ 12 } - \left ( 3 \sqrt{ 2 } \right ) } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } }$
$\dfrac { \sqrt{ 12 } - \left ( 3 \sqrt{ 2 } \right ) } { \color{#FF6800}{ - } 1 }$
$ $ If the denominator is 1, the denominator can be removed $ $
$\color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 12 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right )$
$- \left ( \sqrt{ \color{#FF6800}{ 12 } } - \left ( 3 \sqrt{ 2 } \right ) \right )$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$- \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } - \left ( 3 \sqrt{ 2 } \right ) \right )$
$- \left ( 2 \sqrt{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right )$
$ $ Get rid of unnecessary parentheses $ $
$- \left ( 2 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } }$
Solution search results
search-thumbnail-The rationalizing factor of \sqrt{23} is 
$°$ $Options^{°}$ $0$ 
A 24 
23 
C \sqrt{23} 
D None of these
7th-9th grade
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