$\sqrt{ \color{#FF6800}{ 0.002 } } = x \sqrt{ 5 }$
$ $ Convert decimals to fractions $ $
$\sqrt{ \color{#FF6800}{ \dfrac { 1 } { 500 } } } = x \sqrt{ 5 }$
$\sqrt{ \color{#FF6800}{ \dfrac { 1 } { 500 } } } = x \sqrt{ 5 }$
$ $ Separate the radical sign from the denominator and numerator $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 1 } } { \sqrt{ 500 } } } = x \sqrt{ 5 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 1 } } } { \sqrt{ 500 } } = x \sqrt{ 5 }$
$n $ square root of 1 is 1 $ $
$\dfrac { \color{#FF6800}{ 1 } } { \sqrt{ 500 } } = x \sqrt{ 5 }$
$\dfrac { 1 } { \sqrt{ \color{#FF6800}{ 500 } } } = x \sqrt{ 5 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\dfrac { 1 } { \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 5 } } } = x \sqrt{ 5 }$
$\dfrac { 1 } { 10 \sqrt{ 5 } } = \color{#FF6800}{ x } \sqrt{ \color{#FF6800}{ 5 } }$
$ $ Simplify the expression $ $
$\dfrac { 1 } { 10 \sqrt{ 5 } } = \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ x }$
$\color{#FF6800}{ \dfrac { 1 } { 10 \sqrt{ 5 } } } = \sqrt{ 5 } x$
$ $ Calculate the expression $ $
$\color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 50 } } = \sqrt{ 5 } x$
$\color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 50 } } = \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ x }$
$ $ Organize the expression $ $
$\sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 50 } }$
$\sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 50 } }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 50 \sqrt{ 5 } } }$
$x = \color{#FF6800}{ \dfrac { \sqrt{ 5 } } { 50 \sqrt{ 5 } } }$
$ $ Calculate the expression $ $
$x = \color{#FF6800}{ \dfrac { 1 } { 50 } }$