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Formula
Calculate the value
$\dfrac{ \sqrt{ 2 } }{ 2 } \times \dfrac{ \sqrt{ 2 } }{ 2 } + \dfrac{ \sqrt{ 3 } }{ 2 } \times \dfrac{ 1 }{ 2 } - \dfrac{ 1 }{ 4 }$
$\dfrac { 1 + \sqrt{ 3 } } { 4 }$
Calculate the value
$\color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 2 } } \times \dfrac { \sqrt{ 2 } } { 2 } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$\left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \times \dfrac { \sqrt{ 2 } } { 2 } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
$\left ( \dfrac { \sqrt{ 2 } } { 2 } \right ) ^ { 1 } \times \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$\left ( \dfrac { \sqrt{ 2 } } { 2 } \right ) ^ { 1 } \left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 2 } } \right ) ^ { \color{#FF6800}{ 1 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
$\left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 2 } } \right ) ^ { \color{#FF6800}{ 1 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
 Add the exponent as the base is the same 
$\left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 2 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
$\left ( \dfrac { \sqrt{ 2 } } { 2 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
 Add $1$ and $1$
$\left ( \dfrac { \sqrt{ 2 } } { 2 } \right ) ^ { \color{#FF6800}{ 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
$\left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
 When raising a fraction to the power, raise the numerator and denominator each to the power 
$\dfrac { \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
$\dfrac { \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } } { 2 ^ { 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
 If you square the radical sign, it will disappear 
$\dfrac { \color{#FF6800}{ 2 } } { 2 ^ { 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
$\color{#FF6800}{ \dfrac { 2 } { 2 ^ { 2 } } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
 Reduce the fraction 
$\color{#FF6800}{ \dfrac { 1 } { 2 } } + \dfrac { \sqrt{ 3 } } { 2 } \times \dfrac { 1 } { 2 } - \dfrac { 1 } { 4 }$
$\dfrac { 1 } { 2 } + \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } - \dfrac { 1 } { 4 }$
 Arrange the terms multiplied by fractions 
$\dfrac { 1 } { 2 } + \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 2 \times 2 } } - \dfrac { 1 } { 4 }$
$\dfrac { 1 } { 2 } + \dfrac { \sqrt{ 3 } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } - \dfrac { 1 } { 4 }$
 Multiply $2$ and $2$
$\dfrac { 1 } { 2 } + \dfrac { \sqrt{ 3 } } { \color{#FF6800}{ 4 } } - \dfrac { 1 } { 4 }$
$\color{#FF6800}{ \dfrac { 1 } { 2 } } + \dfrac { \sqrt{ 3 } } { 4 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 4 } }$
 Find the difference between the two fractions $\dfrac { 1 } { 2 }$ and $- \dfrac { 1 } { 4 }$
$\color{#FF6800}{ \dfrac { 1 } { 4 } } + \dfrac { \sqrt{ 3 } } { 4 }$
$\color{#FF6800}{ \dfrac { 1 } { 4 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \sqrt{ 3 } } { 4 } }$
 Combine the fraction with the same denominator 
$\dfrac { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } } { 4 }$
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