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Formula
Solve the equation
Answer
$\sqrt{ 0.005 } = a \sqrt{ 2 }$
$a = \dfrac { 1 } { 20 }$
 Solve a solution to $a$
$\sqrt{ \color{#FF6800}{ 0.005 } } = a \sqrt{ 2 }$
 Convert decimals to fractions 
$\sqrt{ \color{#FF6800}{ \dfrac { 1 } { 200 } } } = a \sqrt{ 2 }$
$\sqrt{ \color{#FF6800}{ \dfrac { 1 } { 200 } } } = a \sqrt{ 2 }$
 Separate the radical sign from the denominator and numerator 
$\color{#FF6800}{ \dfrac { \sqrt{ 1 } } { \sqrt{ 200 } } } = a \sqrt{ 2 }$
$\dfrac { \sqrt{ \color{#FF6800}{ 1 } } } { \sqrt{ 200 } } = a \sqrt{ 2 }$
$n$ square root of 1 is 1 
$\dfrac { \color{#FF6800}{ 1 } } { \sqrt{ 200 } } = a \sqrt{ 2 }$
$\dfrac { 1 } { \sqrt{ \color{#FF6800}{ 200 } } } = a \sqrt{ 2 }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$\dfrac { 1 } { \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 2 } } } = a \sqrt{ 2 }$
$\dfrac { 1 } { 10 \sqrt{ 2 } } = \color{#FF6800}{ a } \sqrt{ \color{#FF6800}{ 2 } }$
 Simplify the expression 
$\dfrac { 1 } { 10 \sqrt{ 2 } } = \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ a }$
$\color{#FF6800}{ \dfrac { 1 } { 10 \sqrt{ 2 } } } = \sqrt{ 2 } a$
 Calculate the expression 
$\color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 20 } } = \sqrt{ 2 } a$
$\color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 20 } } = \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ a }$
 Organize the expression 
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ a } = \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 20 } }$
$\sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ a } = \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 20 } }$
 Divide both sides by the same number 
$\color{#FF6800}{ a } = \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 20 \sqrt{ 2 } } }$
$a = \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 20 \sqrt{ 2 } } }$
 Calculate the expression 
$a = \color{#FF6800}{ \dfrac { 1 } { 20 } }$
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