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Calculate the value
Answer
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$\dfrac{ \sqrt{ 2 } }{ 2 } \times \dfrac{ \sqrt{ 2 } }{ 2 } + \dfrac{ \sqrt{ 3 } }{ 2 } \times \dfrac{ 1 }{ 2 } - \dfrac{ 1 }{ 4 }$
$\dfrac { 1 + \sqrt{ 3 } } { 4 }$
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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