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$32$
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$\left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 5 } } \left ( \dfrac { 1 } { \sqrt{ 3 } - 1 } \right ) ^ { - 5 }$
$ $ Calculate power $ $
$\left ( \color{#FF6800}{ 76 } \color{#FF6800}{ + } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \dfrac { 1 } { \sqrt{ 3 } - 1 } \right ) ^ { - 5 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { 1 } { \sqrt{ 3 } - 1 } \right ) ^ { - 5 }$
$ $ Find the conjugate irrational number of denominator $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } } \right ) ^ { - 5 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { 1 } { \sqrt{ 3 } - 1 } \times \dfrac { \sqrt{ 3 } + 1 } { \sqrt{ 3 } + 1 } \right ) ^ { - 5 }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) } } \right ) ^ { - 5 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { \color{#FF6800}{ 1 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) } { \left ( \sqrt{ 3 } - 1 \right ) \left ( \sqrt{ 3 } + 1 \right ) } \right ) ^ { - 5 }$
$ $ Multiply each term in parentheses by $ 1$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { \color{#FF6800}{ 1 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } { \left ( \sqrt{ 3 } - 1 \right ) \left ( \sqrt{ 3 } + 1 \right ) } \right ) ^ { - 5 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { 1 \sqrt{ 3 } + 1 } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) } \right ) ^ { - 5 }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { 1 \sqrt{ 3 } + 1 } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } } \right ) ^ { - 5 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { 1 \sqrt{ 3 } + 1 } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } - 1 ^ { 2 } } \right ) ^ { - 5 }$
$ $ Calculate power $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { 1 \sqrt{ 3 } + 1 } { \color{#FF6800}{ 3 } - 1 ^ { 2 } } \right ) ^ { - 5 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { 1 \sqrt{ 3 } + 1 } { 3 - \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } } \right ) ^ { - 5 }$
$ $ Calculate power $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { 1 \sqrt{ 3 } + 1 } { 3 - \color{#FF6800}{ 1 } } \right ) ^ { - 5 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { \color{#FF6800}{ 1 } \sqrt{ 3 } + 1 } { 3 - 1 } \right ) ^ { - 5 }$
$ $ Multiplying any number by 1 does not change the value $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { \sqrt{ 3 } + 1 } { 3 - 1 } \right ) ^ { - 5 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { \sqrt{ 3 } + 1 } { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } \right ) ^ { - 5 }$
$ $ Subtract $ 1 $ from $ 3$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \dfrac { \sqrt{ 3 } + 1 } { \color{#FF6800}{ 2 } } \right ) ^ { - 5 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \right ) ^ { \color{#FF6800}{ - } \color{#FF6800}{ 5 } }$
$ $ When raising a fraction to the power, raise the numerator and denominator each to the power $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ - } \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 5 } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { \left ( \sqrt{ 3 } + 1 \right ) ^ { \color{#FF6800}{ - } \color{#FF6800}{ 5 } } } { 2 ^ { - 5 } }$
$ $ If the exponent is negative, change it to a fraction $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { \dfrac { 1 } { \left ( \sqrt{ 3 } + 1 \right ) ^ { 5 } } } { 2 ^ { - 5 } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \color{#FF6800}{ \dfrac { \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 5 } } } } } { \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 5 } } } }$
$ $ Calculate the complex fraction $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 5 } } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 5 } } \times 2 ^ { - 5 } }$
$ $ Calculate power $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \left ( \color{#FF6800}{ 76 } \color{#FF6800}{ + } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \times 2 ^ { - 5 } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \left ( 76 + 44 \sqrt{ 3 } \right ) \times 2 ^ { \color{#FF6800}{ - } \color{#FF6800}{ 5 } } }$
$ $ If the exponent is negative, change it to a fraction $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { 2 ^ { 5 } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 5 } } } }$
$ $ Calculate power $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \color{#FF6800}{ 32 } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \left ( \color{#FF6800}{ 76 } \color{#FF6800}{ + } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 32 } } } }$
$ $ Multiply each term in parentheses by $ \dfrac { 1 } { 32 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \color{#FF6800}{ 76 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 32 } } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 32 } } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \color{#FF6800}{ 76 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 32 } } } + \left ( 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { 32 } }$
$ $ Calculate the product of rational numbers $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 8 } } } + \left ( 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { 32 } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \dfrac { 19 } { 8 } + \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 32 } } } }$
$ $ Get rid of unnecessary parentheses $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \dfrac { 19 } { 8 } + \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 32 } } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \dfrac { 19 } { 8 } + \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 32 } } } }$
$ $ Simplify the expression $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \dfrac { 19 } { 8 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } } { \color{#FF6800}{ 8 } } } \sqrt{ \color{#FF6800}{ 3 } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \dfrac { 19 } { 8 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } } { \color{#FF6800}{ 8 } } } \sqrt{ \color{#FF6800}{ 3 } } }$
$ $ Arrange the terms multiplied by fractions $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \dfrac { 19 } { 8 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 8 } } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 8 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 8 } } } }$
$ $ Combine the fraction with the same denominator $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 1 } { \dfrac { \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } } { 8 } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 8 } } } } }$
$ $ Calculate the complex fraction $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } } { \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 8 } { 19 + 11 \sqrt{ 3 } }$
$ $ Find the conjugate irrational number of denominator $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } } { \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } } } \times \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \color{#FF6800}{ 19 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 8 } { 19 + 11 \sqrt{ 3 } } \times \dfrac { 19 - \left ( 11 \sqrt{ 3 } \right ) } { 19 - \left ( 11 \sqrt{ 3 } \right ) }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } \left ( \color{#FF6800}{ 19 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } { \left ( \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 19 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { \color{#FF6800}{ 8 } \left ( \color{#FF6800}{ 19 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } { \left ( 19 + 11 \sqrt{ 3 } \right ) \left ( 19 - \left ( 11 \sqrt{ 3 } \right ) \right ) }$
$ $ Multiply each term in parentheses by $ 8$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) } { \left ( 19 + 11 \sqrt{ 3 } \right ) \left ( 19 - \left ( 11 \sqrt{ 3 } \right ) \right ) }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 8 \times 19 + 8 \times \left ( - \left ( 11 \sqrt{ 3 } \right ) \right ) } { \left ( \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 19 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 8 \times 19 + 8 \times \left ( - \left ( 11 \sqrt{ 3 } \right ) \right ) } { \color{#FF6800}{ 19 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 8 \times 19 + 8 \times \left ( - \left ( 11 \sqrt{ 3 } \right ) \right ) } { \color{#FF6800}{ 19 } ^ { \color{#FF6800}{ 2 } } - \left ( 11 \sqrt{ 3 } \right ) ^ { 2 } }$
$ $ Calculate power $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 8 \times 19 + 8 \times \left ( - \left ( 11 \sqrt{ 3 } \right ) \right ) } { \color{#FF6800}{ 361 } - \left ( 11 \sqrt{ 3 } \right ) ^ { 2 } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 8 \times 19 + 8 \times \left ( - \left ( 11 \sqrt{ 3 } \right ) \right ) } { 361 - \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 8 \times 19 + 8 \times \left ( - \left ( 11 \sqrt{ 3 } \right ) \right ) } { 361 - \color{#FF6800}{ 363 } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 19 } + 8 \times \left ( - \left ( 11 \sqrt{ 3 } \right ) \right ) } { 361 - 363 }$
$ $ Multiply $ 8 $ and $ 19$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { \color{#FF6800}{ 152 } + 8 \times \left ( - \left ( 11 \sqrt{ 3 } \right ) \right ) } { 361 - 363 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 152 + 8 \times \left ( \color{#FF6800}{ - } \left ( 11 \sqrt{ 3 } \right ) \right ) } { 361 - 363 }$
$ $ Move the (-) sign forward $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 152 \color{#FF6800}{ - } 8 \left ( 11 \sqrt{ 3 } \right ) } { 361 - 363 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 152 \color{#FF6800}{ - } \color{#FF6800}{ 8 } \left ( \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { 361 - 363 }$
$ $ Get rid of unnecessary parentheses $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 152 \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } } { 361 - 363 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 152 \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 11 } \sqrt{ \color{#FF6800}{ 3 } } } { 361 - 363 }$
$ $ Simplify the expression $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 152 \color{#FF6800}{ - } \color{#FF6800}{ 88 } \sqrt{ \color{#FF6800}{ 3 } } } { 361 - 363 }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 152 - 88 \sqrt{ 3 } } { \color{#FF6800}{ 361 } \color{#FF6800}{ - } \color{#FF6800}{ 363 } }$
$ $ Subtract $ 363 $ from $ 361$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 152 - 88 \sqrt{ 3 } } { \color{#FF6800}{ - } \color{#FF6800}{ 2 } }$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \dfrac { 152 - 88 \sqrt{ 3 } } { \color{#FF6800}{ - } \color{#FF6800}{ 2 } }$
$ $ Move the minus sign to the front of the fraction $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 152 } \color{#FF6800}{ - } \color{#FF6800}{ 88 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 2 } } } \right )$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \left ( - \color{#FF6800}{ \dfrac { \color{#FF6800}{ 152 } \color{#FF6800}{ - } \color{#FF6800}{ 88 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 2 } } } \right )$
$ $ Reduce the fraction $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \left ( - \left ( \color{#FF6800}{ 76 } \color{#FF6800}{ - } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right )$
$\left ( 76 + 44 \sqrt{ 3 } \right ) \times \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 76 } \color{#FF6800}{ - } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$\left ( 76 + 44 \sqrt{ 3 } \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ 76 } \color{#FF6800}{ + } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$\left ( \color{#FF6800}{ 76 } \color{#FF6800}{ + } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ 76 } \color{#FF6800}{ + } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\color{#FF6800}{ 76 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 76 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 76 } \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 76 } \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$\color{#FF6800}{ 76 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 76 } \right ) + 76 \left ( 44 \sqrt{ 3 } \right ) + \left ( 44 \sqrt{ 3 } \right ) \times \left ( - 76 \right ) + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$ $ Multiply $ 76 $ and $ - 76$
$\color{#FF6800}{ - } \color{#FF6800}{ 5776 } + 76 \left ( 44 \sqrt{ 3 } \right ) + \left ( 44 \sqrt{ 3 } \right ) \times \left ( - 76 \right ) + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$- 5776 + \color{#FF6800}{ 76 } \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \left ( 44 \sqrt{ 3 } \right ) \times \left ( - 76 \right ) + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$- 5776 + \color{#FF6800}{ 76 } \color{#FF6800}{ \times } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } + \left ( 44 \sqrt{ 3 } \right ) \times \left ( - 76 \right ) + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$- 5776 + \color{#FF6800}{ 76 } \color{#FF6800}{ \times } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } + \left ( 44 \sqrt{ 3 } \right ) \times \left ( - 76 \right ) + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$ $ Simplify the expression $ $
$- 5776 + \color{#FF6800}{ 3344 } \sqrt{ \color{#FF6800}{ 3 } } + \left ( 44 \sqrt{ 3 } \right ) \times \left ( - 76 \right ) + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$- 5776 + 3344 \sqrt{ 3 } + \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 76 } \right ) + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$- 5776 + 3344 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 76 } + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$- 5776 + 3344 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 76 } + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$ $ Simplify the expression $ $
$- 5776 + 3344 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3344 } \sqrt{ \color{#FF6800}{ 3 } } + \left ( 44 \sqrt{ 3 } \right ) \left ( 44 \sqrt{ 3 } \right )$
$- 5776 + 3344 \sqrt{ 3 } - 3344 \sqrt{ 3 } + \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$ $ Get rid of unnecessary parentheses $ $
$- 5776 + 3344 \sqrt{ 3 } - 3344 \sqrt{ 3 } + \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } }$
$- 5776 + 3344 \sqrt{ 3 } - 3344 \sqrt{ 3 } + \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 44 } \sqrt{ \color{#FF6800}{ 3 } }$
$ $ Simplify the expression $ $
$- 5776 + 3344 \sqrt{ 3 } - 3344 \sqrt{ 3 } + \color{#FF6800}{ 5808 }$
$- 5776 \color{#FF6800}{ + } \color{#FF6800}{ 3344 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3344 } \sqrt{ \color{#FF6800}{ 3 } } + 5808$
$ $ Eliminate opponent number $ $
$- 5776 + 5808$
$\color{#FF6800}{ - } \color{#FF6800}{ 5776 } \color{#FF6800}{ + } \color{#FF6800}{ 5808 }$
$ $ Add $ - 5776 $ and $ 5808$
$\color{#FF6800}{ 32 }$
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