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$\dfrac{ 5 }{ \sqrt{ 5 } -2 }$
$5 \sqrt{ 5 } + 10$
Calculate the value
$\dfrac { 5 } { \sqrt{ 5 } - 2 }$
$ $ Find the conjugate irrational number of denominator $ $
$\color{#FF6800}{ \dfrac { 5 } { \sqrt{ 5 } - 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 5 } + 2 } { \sqrt{ 5 } + 2 } }$
$\dfrac { 5 } { \sqrt{ 5 } - 2 } \times \dfrac { \sqrt{ 5 } + 2 } { \sqrt{ 5 } + 2 }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\color{#FF6800}{ \dfrac { 5 \left ( \sqrt{ 5 } + 2 \right ) } { \left ( \sqrt{ 5 } - 2 \right ) \left ( \sqrt{ 5 } + 2 \right ) } }$
$\dfrac { \color{#FF6800}{ 5 } \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) } { \left ( \sqrt{ 5 } - 2 \right ) \left ( \sqrt{ 5 } + 2 \right ) }$
$ $ Multiply each term in parentheses by $ 5$
$\dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } { \left ( \sqrt{ 5 } - 2 \right ) \left ( \sqrt{ 5 } + 2 \right ) }$
$\dfrac { 5 \sqrt{ 5 } + 5 \times 2 } { \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 5 \sqrt{ 5 } + 5 \times 2 } { \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } }$
$\dfrac { 5 \sqrt{ 5 } + 5 \times 2 } { \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } - 2 ^ { 2 } }$
$ $ Calculate power $ $
$\dfrac { 5 \sqrt{ 5 } + 5 \times 2 } { \color{#FF6800}{ 5 } - 2 ^ { 2 } }$
$\dfrac { 5 \sqrt{ 5 } + 5 \times 2 } { 5 - \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$\dfrac { 5 \sqrt{ 5 } + 5 \times 2 } { 5 - \color{#FF6800}{ 4 } }$
$\dfrac { 5 \sqrt{ 5 } + \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } { 5 - 4 }$
$ $ Multiply $ 5 $ and $ 2$
$\dfrac { 5 \sqrt{ 5 } + \color{#FF6800}{ 10 } } { 5 - 4 }$
$\dfrac { 5 \sqrt{ 5 } + 10 } { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$ $ Subtract $ 4 $ from $ 5$
$\dfrac { 5 \sqrt{ 5 } + 10 } { \color{#FF6800}{ 1 } }$
$\dfrac { 5 \sqrt{ 5 } + 10 } { \color{#FF6800}{ 1 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$\color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
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