qanda-logo
apple logogoogle play logo

Calculator search results

Formula
Calculate the value
Answer
circle-check-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
$$\dfrac { \sqrt{ 5 } - 2 } { \sqrt{ 5 } + 2 }$$
$9 - 4 \sqrt{ 5 }$
Calculate the value
$\dfrac { \sqrt{ 5 } - 2 } { \sqrt{ 5 } + 2 }$
$ $ Find the conjugate irrational number of denominator $ $
$\color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } } { \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } } { \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } } }$
$\dfrac { \sqrt{ 5 } - 2 } { \sqrt{ 5 } + 2 } \times \dfrac { \sqrt{ 5 } - 2 } { \sqrt{ 5 } - 2 }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\color{#FF6800}{ \dfrac { \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) } }$
$\dfrac { \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) } { \left ( \sqrt{ 5 } + 2 \right ) \left ( \sqrt{ 5 } - 2 \right ) }$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\dfrac { \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) } { \left ( \sqrt{ 5 } + 2 \right ) \left ( \sqrt{ 5 } - 2 \right ) }$
$\dfrac { \sqrt{ 5 } \sqrt{ 5 } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \left ( \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { \sqrt{ 5 } \sqrt{ 5 } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { \left ( \sqrt{ 5 } \right ) ^ { 2 } - 2 ^ { 2 } }$
$ $ Arrange the expression $ $
$\dfrac { \sqrt{ \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { \left ( \sqrt{ 5 } \right ) ^ { 2 } - 2 ^ { 2 } }$
$\dfrac { \sqrt{ 5 \times 5 } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { \left ( \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } - 2 ^ { 2 } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 5 \times 5 } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { \color{#FF6800}{ 5 } - 2 ^ { 2 } }$
$\dfrac { \sqrt{ 5 \times 5 } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { 5 - \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$\dfrac { \sqrt{ 5 \times 5 } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { 5 - \color{#FF6800}{ 4 } }$
$\dfrac { \sqrt{ \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { 5 - 4 }$
$ $ Multiply $ 5 $ and $ 5$
$\dfrac { \sqrt{ \color{#FF6800}{ 25 } } + \sqrt{ 5 } \left ( - 2 \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { 5 - 4 }$
$\dfrac { \sqrt{ 25 } + \sqrt{ \color{#FF6800}{ 5 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { 5 - 4 }$
$ $ Simplify the expression $ $
$\dfrac { \sqrt{ 25 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } - 2 \sqrt{ 5 } - 2 \times \left ( - 2 \right ) } { 5 - 4 }$
$\dfrac { \sqrt{ 25 } - 2 \sqrt{ 5 } - 2 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) } { 5 - 4 }$
$ $ Multiply $ - 2 $ and $ - 2$
$\dfrac { \sqrt{ 25 } - 2 \sqrt{ 5 } - 2 \sqrt{ 5 } + \color{#FF6800}{ 4 } } { 5 - 4 }$
$\dfrac { \sqrt{ 25 } - 2 \sqrt{ 5 } - 2 \sqrt{ 5 } + 4 } { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$ $ Subtract $ 4 $ from $ 5$
$\dfrac { \sqrt{ 25 } - 2 \sqrt{ 5 } - 2 \sqrt{ 5 } + 4 } { \color{#FF6800}{ 1 } }$
$\dfrac { \sqrt{ 25 } - 2 \sqrt{ 5 } - 2 \sqrt{ 5 } + 4 } { \color{#FF6800}{ 1 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$\sqrt{ \color{#FF6800}{ 25 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$\sqrt{ \color{#FF6800}{ 25 } } - 2 \sqrt{ 5 } - 2 \sqrt{ 5 } + 4$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\color{#FF6800}{ 5 } - 2 \sqrt{ 5 } - 2 \sqrt{ 5 } + 4$
$\color{#FF6800}{ 5 } - 2 \sqrt{ 5 } - 2 \sqrt{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$ $ Add $ 5 $ and $ 4$
$\color{#FF6800}{ 9 } - 2 \sqrt{ 5 } - 2 \sqrt{ 5 }$
$9 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } }$
$ $ Calculate between similar terms $ $
$9 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt{ \color{#FF6800}{ 5 } }$
Try more features at Qanda!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture
apple logogoogle play logo