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$\dfrac{ \sqrt{ 2 } }{ 5-2 \sqrt{ 6 } } - \dfrac{ \sqrt{ 2 } }{ 5+2 \sqrt{ 6 } }$
$8 \sqrt{ 3 }$
Calculate the value
$\dfrac { \sqrt{ 2 } } { 5 - 2 \sqrt{ 6 } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Find the conjugate irrational number of denominator $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 5 - 2 \sqrt{ 6 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 5 - \left ( - 2 \sqrt{ 6 } \right ) } { 5 - \left ( - 2 \sqrt{ 6 } \right ) } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { \sqrt{ 2 } } { 5 - 2 \sqrt{ 6 } } \times \dfrac { 5 - \left ( - 2 \sqrt{ 6 } \right ) } { 5 - \left ( - 2 \sqrt{ 6 } \right ) } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 2 } \left ( 5 - \left ( - 2 \sqrt{ 6 } \right ) \right ) } { \left ( 5 - 2 \sqrt{ 6 } \right ) \left ( 5 - \left ( - 2 \sqrt{ 6 } \right ) \right ) } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \right ) } { \left ( 5 - 2 \sqrt{ 6 } \right ) \left ( 5 - \left ( - 2 \sqrt{ 6 } \right ) \right ) } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Multiply each term in parentheses by $ \sqrt{ 2 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \right ) } { \left ( 5 - 2 \sqrt{ 6 } \right ) \left ( 5 - \left ( - 2 \sqrt{ 6 } \right ) \right ) } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( - 2 \sqrt{ 6 } \right ) \right ) } { \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \right ) } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( - 2 \sqrt{ 6 } \right ) \right ) } { \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 2 } } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( - 2 \sqrt{ 6 } \right ) \right ) } { \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } - \left ( 2 \sqrt{ 6 } \right ) ^ { 2 } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( - 2 \sqrt{ 6 } \right ) \right ) } { \color{#FF6800}{ 25 } - \left ( 2 \sqrt{ 6 } \right ) ^ { 2 } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( - 2 \sqrt{ 6 } \right ) \right ) } { 25 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 2 } } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( - 2 \sqrt{ 6 } \right ) \right ) } { 25 - \color{#FF6800}{ 24 } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } + \sqrt{ 2 } \times \left ( - \left ( - 2 \sqrt{ 6 } \right ) \right ) } { 25 - 24 } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Simplify the expression $ $
$\dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \left ( - 2 \sqrt{ 6 } \right ) \right ) } { 25 - 24 } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { 5 \sqrt{ 2 } + \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \left ( - 2 \sqrt{ 6 } \right ) \right ) } { 25 - 24 } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Move the (-) sign forward $ $
$\dfrac { 5 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ 2 } \times \left ( - 2 \sqrt{ 6 } \right ) } { 25 - 24 } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { 5 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) } { 25 - 24 } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 5 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \sqrt{ \color{#FF6800}{ 6 } } } { 25 - 24 } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { 5 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \sqrt{ \color{#FF6800}{ 6 } } } { 25 - 24 } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Simplify the expression $ $
$\dfrac { 5 \sqrt{ 2 } + \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } } { 25 - 24 } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { 5 \sqrt{ 2 } + 4 \sqrt{ 3 } } { \color{#FF6800}{ 25 } \color{#FF6800}{ - } \color{#FF6800}{ 24 } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Subtract $ 24 $ from $ 25$
$\dfrac { 5 \sqrt{ 2 } + 4 \sqrt{ 3 } } { \color{#FF6800}{ 1 } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$\dfrac { 5 \sqrt{ 2 } + 4 \sqrt{ 3 } } { \color{#FF6800}{ 1 } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$\color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } }$
$ $ Find the conjugate irrational number of denominator $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 5 - \left ( 2 \sqrt{ 6 } \right ) } { 5 - \left ( 2 \sqrt{ 6 } \right ) } } \right )$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \left ( \dfrac { \sqrt{ 2 } } { 5 + 2 \sqrt{ 6 } } \times \dfrac { 5 - \left ( 2 \sqrt{ 6 } \right ) } { 5 - \left ( 2 \sqrt{ 6 } \right ) } \right )$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \color{#FF6800}{ \dfrac { \sqrt{ 2 } \left ( 5 - \left ( 2 \sqrt{ 6 } \right ) \right ) } { \left ( 5 + 2 \sqrt{ 6 } \right ) \left ( 5 - \left ( 2 \sqrt{ 6 } \right ) \right ) } }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \right ) } { \left ( 5 + 2 \sqrt{ 6 } \right ) \left ( 5 - \left ( 2 \sqrt{ 6 } \right ) \right ) }$
$ $ Multiply each term in parentheses by $ \sqrt{ 2 }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \right ) } { \left ( 5 + 2 \sqrt{ 6 } \right ) \left ( 5 - \left ( 2 \sqrt{ 6 } \right ) \right ) }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( 2 \sqrt{ 6 } \right ) \right ) } { \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( 2 \sqrt{ 6 } \right ) \right ) } { \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( 2 \sqrt{ 6 } \right ) \right ) } { \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } - \left ( 2 \sqrt{ 6 } \right ) ^ { 2 } }$
$ $ Calculate power $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( 2 \sqrt{ 6 } \right ) \right ) } { \color{#FF6800}{ 25 } - \left ( 2 \sqrt{ 6 } \right ) ^ { 2 } }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( 2 \sqrt{ 6 } \right ) \right ) } { 25 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ 2 } \times 5 + \sqrt{ 2 } \times \left ( - \left ( 2 \sqrt{ 6 } \right ) \right ) } { 25 - \color{#FF6800}{ 24 } }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } + \sqrt{ 2 } \times \left ( - \left ( 2 \sqrt{ 6 } \right ) \right ) } { 25 - 24 }$
$ $ Simplify the expression $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \left ( 2 \sqrt{ 6 } \right ) \right ) } { 25 - 24 }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { 5 \sqrt{ 2 } + \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \left ( 2 \sqrt{ 6 } \right ) \right ) } { 25 - 24 }$
$ $ Move the (-) sign forward $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { 5 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ 2 } \left ( 2 \sqrt{ 6 } \right ) } { 25 - 24 }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { 5 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) } { 25 - 24 }$
$ $ Get rid of unnecessary parentheses $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { 5 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } } { 25 - 24 }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { 5 \sqrt{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } } { 25 - 24 }$
$ $ Simplify the expression $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { 5 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } } { 25 - 24 }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { 5 \sqrt{ 2 } - 4 \sqrt{ 3 } } { \color{#FF6800}{ 25 } \color{#FF6800}{ - } \color{#FF6800}{ 24 } }$
$ $ Subtract $ 24 $ from $ 25$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { 5 \sqrt{ 2 } - 4 \sqrt{ 3 } } { \color{#FF6800}{ 1 } }$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \dfrac { 5 \sqrt{ 2 } - 4 \sqrt{ 3 } } { \color{#FF6800}{ 1 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } - \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$5 \sqrt{ 2 } + 4 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } }$
$\color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } + 4 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } + 4 \sqrt{ 3 }$
$ $ Eliminate opponent number $ $
$4 \sqrt{ 3 } + 4 \sqrt{ 3 }$
$\color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 3 } }$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ 8 } \sqrt{ \color{#FF6800}{ 3 } }$
Solution search results
search-thumbnail-$\dfrac {5-2\sqrt{6} } {5+2\sqrt{6} }-=a+b\sqrt{6} $ Find a and b.
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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