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Formula
Calculate the value
Answer
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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 $ $
$\color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
Solution search results
search-thumbnail-$h=\dfrac {\dfrac {\sqrt{5} -2} {\sqrt{5} -1}} {\dfrac {\sqrt{5} +2} {2\sqrt{5} -2}}$
7th-9th grade
Algebra
search-thumbnail-Can you answer this? 
$20$ $25$ 

$18$ 

$\left($ 
$\left(A\right)$ $A\right)2$ 
$21frac\left(5\right)\left(9\right)$ \) 
$\left(B\right)$ $B\right)$ $1\left(211$ 
$\left(C\right)$ $1\left(21$ $21+rac\left(7\right)+9\right)$ \) 
$\left(D\right)$ $1\left(2\right)$ 2\frac{8}{9} 
$ac\left(8\right)\left(9\right)$ \) $9:18PM\sqrt{} $
1st-6th 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
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