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$\dfrac{ \sqrt{ 7 } + \sqrt{ 5 } }{ \sqrt{ 7 } - \sqrt{ 5 } } + \dfrac{ \sqrt{ 7 } - \sqrt{ 5 } }{ \sqrt{ 7 } + \sqrt{ 5 } }$
$12$
Calculate the value
$\dfrac { \sqrt{ 7 } + \sqrt{ 5 } } { \sqrt{ 7 } - \sqrt{ 5 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Find the conjugate irrational number of denominator $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 7 } + \sqrt{ 5 } } { \sqrt{ 7 } - \sqrt{ 5 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 7 } + \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 7 } + \sqrt{ 5 } } { \sqrt{ 7 } - \sqrt{ 5 } } \times \dfrac { \sqrt{ 7 } + \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\color{#FF6800}{ \dfrac { \left ( \sqrt{ 7 } + \sqrt{ 5 } \right ) \left ( \sqrt{ 7 } + \sqrt{ 5 } \right ) } { \left ( \sqrt{ 7 } - \sqrt{ 5 } \right ) \left ( \sqrt{ 7 } + \sqrt{ 5 } \right ) } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { \left ( \sqrt{ 7 } - \sqrt{ 5 } \right ) \left ( \sqrt{ 7 } + \sqrt{ 5 } \right ) } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\dfrac { \sqrt{ \color{#FF6800}{ 7 } } \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 7 } } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } } } { \left ( \sqrt{ 7 } - \sqrt{ 5 } \right ) \left ( \sqrt{ 7 } + \sqrt{ 5 } \right ) } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 7 } \sqrt{ 7 } + \sqrt{ 7 } \sqrt{ 5 } + \sqrt{ 5 } \sqrt{ 7 } + \sqrt{ 5 } \sqrt{ 5 } } { \left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \right ) } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { \sqrt{ 7 } \sqrt{ 7 } + \sqrt{ 7 } \sqrt{ 5 } + \sqrt{ 5 } \sqrt{ 7 } + \sqrt{ 5 } \sqrt{ 5 } } { \left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 7 } } \sqrt{ \color{#FF6800}{ 7 } } + \sqrt{ 7 } \sqrt{ 5 } + \sqrt{ 5 } \sqrt{ 7 } + \sqrt{ 5 } \sqrt{ 5 } } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Arrange the expression $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } } + \sqrt{ 7 } \sqrt{ 5 } + \sqrt{ 5 } \sqrt{ 7 } + \sqrt{ 5 } \sqrt{ 5 } } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ \color{#FF6800}{ 7 } } \sqrt{ \color{#FF6800}{ 5 } } + \sqrt{ 5 } \sqrt{ 7 } + \sqrt{ 5 } \sqrt{ 5 } } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Arrange the expression $ $
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } + \sqrt{ 5 } \sqrt{ 7 } + \sqrt{ 5 } \sqrt{ 5 } } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 \times 5 } + \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 7 } } + \sqrt{ 5 } \sqrt{ 5 } } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Arrange the expression $ $
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 \times 5 } + \sqrt{ \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } } + \sqrt{ 5 } \sqrt{ 5 } } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 \times 5 } + \sqrt{ 5 \times 7 } + \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } } } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Arrange the expression $ $
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 \times 5 } + \sqrt{ 5 \times 7 } + \sqrt{ \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 \times 5 } + \sqrt{ 5 \times 7 } + \sqrt{ 5 \times 5 } } { \left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 \times 5 } + \sqrt{ 5 \times 7 } + \sqrt{ 5 \times 5 } } { \color{#FF6800}{ 7 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 \times 5 } + \sqrt{ 5 \times 7 } + \sqrt{ 5 \times 5 } } { 7 - \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 \times 5 } + \sqrt{ 5 \times 7 } + \sqrt{ 5 \times 5 } } { 7 - \color{#FF6800}{ 5 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } } + \sqrt{ 7 \times 5 } + \sqrt{ 5 \times 7 } + \sqrt{ 5 \times 5 } } { 7 - 5 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Multiply $ 7 $ and $ 7$
$\dfrac { \sqrt{ \color{#FF6800}{ 49 } } + \sqrt{ 7 \times 5 } + \sqrt{ 5 \times 7 } + \sqrt{ 5 \times 5 } } { 7 - 5 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 49 } + \sqrt{ \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } + \sqrt{ 5 \times 7 } + \sqrt{ 5 \times 5 } } { 7 - 5 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Multiply $ 7 $ and $ 5$
$\dfrac { \sqrt{ 49 } + \sqrt{ \color{#FF6800}{ 35 } } + \sqrt{ 5 \times 7 } + \sqrt{ 5 \times 5 } } { 7 - 5 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 49 } + \sqrt{ 35 } + \sqrt{ \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } } + \sqrt{ 5 \times 5 } } { 7 - 5 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Multiply $ 5 $ and $ 7$
$\dfrac { \sqrt{ 49 } + \sqrt{ 35 } + \sqrt{ \color{#FF6800}{ 35 } } + \sqrt{ 5 \times 5 } } { 7 - 5 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 49 } + \sqrt{ 35 } + \sqrt{ 35 } + \sqrt{ \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } } { 7 - 5 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Multiply $ 5 $ and $ 5$
$\dfrac { \sqrt{ 49 } + \sqrt{ 35 } + \sqrt{ 35 } + \sqrt{ \color{#FF6800}{ 25 } } } { 7 - 5 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ 49 } + \sqrt{ 35 } + \sqrt{ 35 } + \sqrt{ 25 } } { \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Subtract $ 5 $ from $ 7$
$\dfrac { \sqrt{ 49 } + \sqrt{ 35 } + \sqrt{ 35 } + \sqrt{ 25 } } { \color{#FF6800}{ 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 49 } } + \sqrt{ 35 } + \sqrt{ 35 } + \sqrt{ 25 } } { 2 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\dfrac { \color{#FF6800}{ 7 } + \sqrt{ 35 } + \sqrt{ 35 } + \sqrt{ 25 } } { 2 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { 7 + \sqrt{ 35 } + \sqrt{ 35 } + \sqrt{ \color{#FF6800}{ 25 } } } { 2 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\dfrac { 7 + \sqrt{ 35 } + \sqrt{ 35 } + \color{#FF6800}{ 5 } } { 2 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { \color{#FF6800}{ 7 } + \sqrt{ 35 } + \sqrt{ 35 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } } { 2 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Add $ 7 $ and $ 5$
$\dfrac { \color{#FF6800}{ 12 } + \sqrt{ 35 } + \sqrt{ 35 } } { 2 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\dfrac { 12 + \sqrt{ \color{#FF6800}{ 35 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 35 } } } { 2 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Calculate between similar terms $ $
$\dfrac { 12 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 35 } } } { 2 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$\color{#FF6800}{ \dfrac { 12 + 2 \sqrt{ 35 } } { 2 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Reduce the fraction $ $
$\color{#FF6800}{ 6 } + \sqrt{ \color{#FF6800}{ 35 } } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } }$
$ $ Find the conjugate irrational number of denominator $ $
$6 + \sqrt{ 35 } + \color{#FF6800}{ \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } - \sqrt{ 5 } } }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } + \sqrt{ 5 } } \times \dfrac { \sqrt{ 7 } - \sqrt{ 5 } } { \sqrt{ 7 } - \sqrt{ 5 } }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$6 + \sqrt{ 35 } + \color{#FF6800}{ \dfrac { \left ( \sqrt{ 7 } - \sqrt{ 5 } \right ) \left ( \sqrt{ 7 } - \sqrt{ 5 } \right ) } { \left ( \sqrt{ 7 } + \sqrt{ 5 } \right ) \left ( \sqrt{ 7 } - \sqrt{ 5 } \right ) } }$
$6 + \sqrt{ 35 } + \dfrac { \left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { \left ( \sqrt{ 7 } + \sqrt{ 5 } \right ) \left ( \sqrt{ 7 } - \sqrt{ 5 } \right ) }$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ \color{#FF6800}{ 7 } } \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { \left ( \sqrt{ 7 } + \sqrt{ 5 } \right ) \left ( \sqrt{ 7 } - \sqrt{ 5 } \right ) }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 7 } \sqrt{ 7 } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 7 } \sqrt{ 7 } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ \color{#FF6800}{ 7 } } \sqrt{ \color{#FF6800}{ 7 } } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } }$
$ $ Arrange the expression $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { \left ( \sqrt{ 7 } \right ) ^ { 2 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 7 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \sqrt{ 5 } \right ) ^ { 2 } }$
$ $ Calculate power $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { \color{#FF6800}{ 7 } - \left ( \sqrt{ 5 } \right ) ^ { 2 } }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 7 \times 7 } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - \color{#FF6800}{ 5 } }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - 5 }$
$ $ Multiply $ 7 $ and $ 7$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ \color{#FF6800}{ 49 } } + \sqrt{ 7 } \times \left ( - \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - 5 }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } + \sqrt{ 7 } \times \left ( \color{#FF6800}{ - } \sqrt{ 5 } \right ) - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - 5 }$
$ $ Move the (-) sign forward $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } \color{#FF6800}{ - } \sqrt{ 7 } \sqrt{ 5 } - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - 5 }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 7 } } \sqrt{ \color{#FF6800}{ 5 } } - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - 5 }$
$ $ Calculate multiplication $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 35 } } - \sqrt{ 5 } \sqrt{ 7 } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - 5 }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 7 } } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - 5 }$
$ $ Calculate multiplication $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 35 } } - \sqrt{ 5 } \times \left ( - \sqrt{ 5 } \right ) } { 7 - 5 }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } \color{#FF6800}{ - } \sqrt{ 5 } \times \left ( \color{#FF6800}{ - } \sqrt{ 5 } \right ) } { 7 - 5 }$
$ $ Since negative numbers are multiplied by an even number, remove the (-) sign $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \sqrt{ 5 } \sqrt{ 5 } } { 7 - 5 }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ 5 } } { 7 - 5 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 5 } } { 7 - 5 }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ 5 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 5 } } } { 7 - 5 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ 5 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 7 - 5 }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } } } { 7 - 5 }$
$ $ Add the exponent as the base is the same $ $
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 7 - 5 }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ 5 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } { 7 - 5 }$
$ $ Add $ 1 $ and $ 1$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ 5 } \right ) ^ { \color{#FF6800}{ 2 } } } { 7 - 5 }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ 5 } \right ) ^ { 2 } } { \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } }$
$ $ Subtract $ 5 $ from $ 7$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ 49 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ 5 } \right ) ^ { 2 } } { \color{#FF6800}{ 2 } }$
$6 + \sqrt{ 35 } + \dfrac { \sqrt{ \color{#FF6800}{ 49 } } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ 5 } \right ) ^ { 2 } } { 2 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$6 + \sqrt{ 35 } + \dfrac { \color{#FF6800}{ 7 } - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ 5 } \right ) ^ { 2 } } { 2 }$
$6 + \sqrt{ 35 } + \dfrac { 7 - \sqrt{ 35 } - \sqrt{ 35 } + \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } } { 2 }$
$ $ If you square the radical sign, it will disappear $ $
$6 + \sqrt{ 35 } + \dfrac { 7 - \sqrt{ 35 } - \sqrt{ 35 } + \color{#FF6800}{ 5 } } { 2 }$
$6 + \sqrt{ 35 } + \dfrac { \color{#FF6800}{ 7 } - \sqrt{ 35 } - \sqrt{ 35 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } } { 2 }$
$ $ Add $ 7 $ and $ 5$
$6 + \sqrt{ 35 } + \dfrac { \color{#FF6800}{ 12 } - \sqrt{ 35 } - \sqrt{ 35 } } { 2 }$
$6 + \sqrt{ 35 } + \dfrac { 12 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 35 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 35 } } } { 2 }$
$ $ Calculate between similar terms $ $
$6 + \sqrt{ 35 } + \dfrac { 12 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 35 } } } { 2 }$
$6 + \sqrt{ 35 } + \color{#FF6800}{ \dfrac { 12 - 2 \sqrt{ 35 } } { 2 } }$
$ $ Reduce the fraction $ $
$6 + \sqrt{ 35 } + \color{#FF6800}{ 6 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 35 } }$
$6 \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 35 } } + 6 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 35 } }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$6 + 6$
$\color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$ $ Add $ 6 $ and $ 6$
$\color{#FF6800}{ 12 }$
Solution search results
search-thumbnail-$\bar{\sqrt{7} -} $ $\sqrt{7} +\sqrt{5} $ $\dfrac {+\sqrt{5} } {-\sqrt{5} }+\dfrac {\sqrt{7} -\sqrt{5} } {\sqrt{7} +\sqrt{5} }$
7th-9th grade
Calculus
search-thumbnail-$B=\dfrac {\sqrt{5} } {\sqrt{7} -\sqrt{5} }+\dfrac {\sqrt{7} } {\sqrt{7} +\sqrt{5} }$
7th-9th grade
Other
search-thumbnail-$\left(\dfrac {\sqrt{7} +\sqrt{5} } {\sqrt{7} -\sqrt{5} }+\dfrac {\sqrt{7} -\sqrt{5} } {\sqrt{7} +\sqrt{5} }\right)=2$
10th-13th grade
Other
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