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$\dfrac{ \sqrt{ 2 } - \sqrt{ 3 } }{ \sqrt{ 2 } + \sqrt{ 3 } } - \dfrac{ \sqrt{ 2 } + \sqrt{ 3 } }{ \sqrt{ 2 } - \sqrt{ 3 } }$
$4 \sqrt{ 6 }$
Calculate the value
$\dfrac { \sqrt{ 2 } - \sqrt{ 3 } } { \sqrt{ 2 } + \sqrt{ 3 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Find the conjugate irrational number of denominator $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 2 } - \sqrt{ 3 } } { \sqrt{ 2 } + \sqrt{ 3 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 2 } - \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 2 } - \sqrt{ 3 } } { \sqrt{ 2 } + \sqrt{ 3 } } \times \dfrac { \sqrt{ 2 } - \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\color{#FF6800}{ \dfrac { \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) } { \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\dfrac { \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 2 } \sqrt{ 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { \sqrt{ 2 } \sqrt{ 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Arrange the expression $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \sqrt{ 3 } \right ) ^ { 2 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { \color{#FF6800}{ 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - \color{#FF6800}{ 3 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Multiply $ 2 $ and $ 2$
$\dfrac { \sqrt{ \color{#FF6800}{ 4 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } + \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \sqrt{ 3 } \right ) - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Move the (-) sign forward $ $
$\dfrac { \sqrt{ 4 } \color{#FF6800}{ - } \sqrt{ 2 } \sqrt{ 3 } - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Calculate multiplication $ $
$\dfrac { \sqrt{ 4 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } - \sqrt{ 3 } \sqrt{ 2 } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Calculate multiplication $ $
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } - \sqrt{ 3 } \times \left ( - \sqrt{ 3 } \right ) } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } \color{#FF6800}{ - } \sqrt{ 3 } \times \left ( \color{#FF6800}{ - } \sqrt{ 3 } \right ) } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Since negative numbers are multiplied by an even number, remove the (-) sign $ $
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \sqrt{ 3 } \sqrt{ 3 } } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ 3 } } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 } } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 3 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 3 } } } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 3 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Add the exponent as the base is the same $ $
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Add $ 1 $ and $ 1$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } } { 2 - 3 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 3 } \right ) ^ { 2 } } { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Subtract $ 3 $ from $ 2$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 3 } \right ) ^ { 2 } } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\dfrac { \sqrt{ 4 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 3 } \right ) ^ { 2 } } { \color{#FF6800}{ - } 1 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$\color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 4 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$- \left ( \sqrt{ \color{#FF6800}{ 4 } } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 3 } \right ) ^ { 2 } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$- \left ( \color{#FF6800}{ 2 } - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ 3 } \right ) ^ { 2 } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$- \left ( 2 - \sqrt{ 6 } - \sqrt{ 6 } + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ If you square the radical sign, it will disappear $ $
$- \left ( 2 - \sqrt{ 6 } - \sqrt{ 6 } + \color{#FF6800}{ 3 } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$- \left ( \color{#FF6800}{ 2 } - \sqrt{ 6 } - \sqrt{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Add $ 2 $ and $ 3$
$- \left ( \color{#FF6800}{ 5 } - \sqrt{ 6 } - \sqrt{ 6 } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$- \left ( 5 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Calculate between similar terms $ $
$- \left ( 5 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } }$
$ $ Find the conjugate irrational number of denominator $ $
$- 5 + 2 \sqrt{ 6 } - \left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } + \sqrt{ 3 } } } \right )$
$- 5 + 2 \sqrt{ 6 } - \left ( \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } - \sqrt{ 3 } } \times \dfrac { \sqrt{ 2 } + \sqrt{ 3 } } { \sqrt{ 2 } + \sqrt{ 3 } } \right )$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$- 5 + 2 \sqrt{ 6 } - \color{#FF6800}{ \dfrac { \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) } { \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) }$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 3 } } } { \left ( \sqrt{ 2 } - \sqrt{ 3 } \right ) \left ( \sqrt{ 2 } + \sqrt{ 3 } \right ) }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 } \sqrt{ 2 } + \sqrt{ 2 } \sqrt{ 3 } + \sqrt{ 3 } \sqrt{ 2 } + \sqrt{ 3 } \sqrt{ 3 } } { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 } \sqrt{ 2 } + \sqrt{ 2 } \sqrt{ 3 } + \sqrt{ 3 } \sqrt{ 2 } + \sqrt{ 3 } \sqrt{ 3 } } { \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \sqrt{ 3 } + \sqrt{ 3 } \sqrt{ 2 } + \sqrt{ 3 } \sqrt{ 3 } } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$ $ Arrange the expression $ $
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } + \sqrt{ 2 } \sqrt{ 3 } + \sqrt{ 3 } \sqrt{ 2 } + \sqrt{ 3 } \sqrt{ 3 } } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 3 } \sqrt{ 2 } + \sqrt{ 3 } \sqrt{ 3 } } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$ $ Arrange the expression $ $
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } + \sqrt{ 3 } \sqrt{ 2 } + \sqrt{ 3 } \sqrt{ 3 } } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 \times 3 } + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 3 } \sqrt{ 3 } } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$ $ Arrange the expression $ $
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 \times 3 } + \sqrt{ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } + \sqrt{ 3 } \sqrt{ 3 } } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 \times 3 } + \sqrt{ 3 \times 2 } + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 3 } } } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$ $ Arrange the expression $ $
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 \times 3 } + \sqrt{ 3 \times 2 } + \sqrt{ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } } { \left ( \sqrt{ 2 } \right ) ^ { 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 \times 3 } + \sqrt{ 3 \times 2 } + \sqrt{ 3 \times 3 } } { \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$ $ Calculate power $ $
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 \times 3 } + \sqrt{ 3 \times 2 } + \sqrt{ 3 \times 3 } } { \color{#FF6800}{ 2 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 \times 3 } + \sqrt{ 3 \times 2 } + \sqrt{ 3 \times 3 } } { 2 - \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 2 \times 2 } + \sqrt{ 2 \times 3 } + \sqrt{ 3 \times 2 } + \sqrt{ 3 \times 3 } } { 2 - \color{#FF6800}{ 3 } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } + \sqrt{ 2 \times 3 } + \sqrt{ 3 \times 2 } + \sqrt{ 3 \times 3 } } { 2 - 3 }$
$ $ Multiply $ 2 $ and $ 2$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ \color{#FF6800}{ 4 } } + \sqrt{ 2 \times 3 } + \sqrt{ 3 \times 2 } + \sqrt{ 3 \times 3 } } { 2 - 3 }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 4 } + \sqrt{ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } + \sqrt{ 3 \times 2 } + \sqrt{ 3 \times 3 } } { 2 - 3 }$
$ $ Multiply $ 2 $ and $ 3$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 4 } + \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 3 \times 2 } + \sqrt{ 3 \times 3 } } { 2 - 3 }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 4 } + \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } + \sqrt{ 3 \times 3 } } { 2 - 3 }$
$ $ Multiply $ 3 $ and $ 2$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 4 } + \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 3 \times 3 } } { 2 - 3 }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 4 } + \sqrt{ 6 } + \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } } { 2 - 3 }$
$ $ Multiply $ 3 $ and $ 3$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 4 } + \sqrt{ 6 } + \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 9 } } } { 2 - 3 }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 4 } + \sqrt{ 6 } + \sqrt{ 6 } + \sqrt{ 9 } } { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } }$
$ $ Subtract $ 3 $ from $ 2$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 4 } + \sqrt{ 6 } + \sqrt{ 6 } + \sqrt{ 9 } } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } }$
$- 5 + 2 \sqrt{ 6 } - \dfrac { \sqrt{ 4 } + \sqrt{ 6 } + \sqrt{ 6 } + \sqrt{ 9 } } { \color{#FF6800}{ - } 1 }$
$ $ If the denominator is 1, the denominator can be removed $ $
$- 5 + 2 \sqrt{ 6 } - \left ( \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 9 } } \right ) \right )$
$- 5 + 2 \sqrt{ 6 } - \left ( - \left ( \sqrt{ \color{#FF6800}{ 4 } } + \sqrt{ 6 } + \sqrt{ 6 } + \sqrt{ 9 } \right ) \right )$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$- 5 + 2 \sqrt{ 6 } - \left ( - \left ( \color{#FF6800}{ 2 } + \sqrt{ 6 } + \sqrt{ 6 } + \sqrt{ 9 } \right ) \right )$
$- 5 + 2 \sqrt{ 6 } - \left ( - \left ( 2 + \sqrt{ 6 } + \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 9 } } \right ) \right )$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$- 5 + 2 \sqrt{ 6 } - \left ( - \left ( 2 + \sqrt{ 6 } + \sqrt{ 6 } + \color{#FF6800}{ 3 } \right ) \right )$
$- 5 + 2 \sqrt{ 6 } - \left ( - \left ( \color{#FF6800}{ 2 } + \sqrt{ 6 } + \sqrt{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \right )$
$ $ Add $ 2 $ and $ 3$
$- 5 + 2 \sqrt{ 6 } - \left ( - \left ( \color{#FF6800}{ 5 } + \sqrt{ 6 } + \sqrt{ 6 } \right ) \right )$
$- 5 + 2 \sqrt{ 6 } - \left ( - \left ( 5 + \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } } \right ) \right )$
$ $ Calculate between similar terms $ $
$- 5 + 2 \sqrt{ 6 } - \left ( - \left ( 5 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \right )$
$- 5 + 2 \sqrt{ 6 } - \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right ) \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$- 5 + 2 \sqrt{ 6 } - \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right )$
$- 5 + 2 \sqrt{ 6 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$- 5 + 2 \sqrt{ 6 } + \color{#FF6800}{ 5 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } }$
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } + 2 \sqrt{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } + 2 \sqrt{ 6 }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$2 \sqrt{ 6 } + 2 \sqrt{ 6 }$
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 6 } }$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 6 } }$
Solution search results
search-thumbnail-$\dfrac {x^{3}} {3\sqrt{3} }$ $-\dfrac {y^{3}} {8}$ $-\dfrac {x^{2}y} {2}+\dfrac {\sqrt{3} } {4}xy^{2}$
7th-9th grade
Algebra
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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