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$\sqrt{ 10 } - 2$
Calculate the value
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \sqrt{ \color{#FF6800}{ 5 } } } } \left ( \sqrt{ 2 } - \sqrt{ 5 } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Calculate the expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } } \left ( \sqrt{ 2 } - \sqrt{ 5 } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Multiply each term in parentheses by $ \dfrac { 2 \sqrt{ 5 } } { 5 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } } \sqrt{ \color{#FF6800}{ 2 } } + \dfrac { 2 \sqrt{ 5 } } { 5 } \times \left ( - \sqrt{ 5 } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Arrange the terms multiplied by fractions $ $
$\color{#FF6800}{ \dfrac { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 5 } } } + \dfrac { 2 \sqrt{ 5 } } { 5 } \times \left ( - \sqrt{ 5 } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\dfrac { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \sqrt{ \color{#FF6800}{ 2 } } } { 5 } + \dfrac { 2 \sqrt{ 5 } } { 5 } \times \left ( - \sqrt{ 5 } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 2 } } } { 5 } + \dfrac { 2 \sqrt{ 5 } } { 5 } \times \left ( - \sqrt{ 5 } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 2 } } } { 5 } + \dfrac { 2 \sqrt{ 5 } } { 5 } \times \left ( - \sqrt{ 5 } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Simplify the expression $ $
$\dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } } } { 5 } + \dfrac { 2 \sqrt{ 5 } } { 5 } \times \left ( - \sqrt{ 5 } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } + \dfrac { 2 \sqrt{ 5 } } { 5 } \times \left ( \color{#FF6800}{ - } \sqrt{ 5 } \right ) + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Move the (-) sign forward $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } \color{#FF6800}{ - } \dfrac { 2 \sqrt{ 5 } } { 5 } \sqrt{ 5 } + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } } \sqrt{ \color{#FF6800}{ 5 } } + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Arrange the terms multiplied by fractions $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \sqrt{ \color{#FF6800}{ 5 } } } { \color{#FF6800}{ 5 } } } + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - \dfrac { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \sqrt{ \color{#FF6800}{ 5 } } } { 5 } + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } } } { 5 } + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } \sqrt{ \color{#FF6800}{ 5 } } } { 5 } + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Simplify the expression $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - \dfrac { \color{#FF6800}{ 10 } } { 5 } + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - \color{#FF6800}{ \dfrac { \color{#FF6800}{ 10 } } { \color{#FF6800}{ 5 } } } + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Reduce the fraction $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - \color{#FF6800}{ 2 } + \dfrac { 1 } { \sqrt{ 7 } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \sqrt{ \color{#FF6800}{ 7 } } } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$ $ Calculate the expression $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 7 } } } { \color{#FF6800}{ 7 } } } \left ( \sqrt{ 14 } + \dfrac { 3 \sqrt{ 70 } } { 5 } \right ) - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { \sqrt{ 7 } } { 7 } \left ( \sqrt{ \color{#FF6800}{ 14 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 70 } } } { \color{#FF6800}{ 5 } } } \right ) - \sqrt{ 2 }$
$ $ Find the sum of the fractions $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { \sqrt{ 7 } } { 7 } \times \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 14 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 70 } } } { \color{#FF6800}{ 5 } } } - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 7 } } } { \color{#FF6800}{ 7 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 14 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 70 } } } { \color{#FF6800}{ 5 } } } - \sqrt{ 2 }$
$ $ Arrange the terms multiplied by fractions $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \color{#FF6800}{ \dfrac { \sqrt{ \color{#FF6800}{ 7 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 14 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 70 } } \right ) } { \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } } - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { \sqrt{ \color{#FF6800}{ 7 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 14 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 70 } } \right ) } { 7 \times 5 } - \sqrt{ 2 }$
$ $ Multiply each term in parentheses by $ \sqrt{ 7 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { \sqrt{ \color{#FF6800}{ 7 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 14 } } \right ) \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 7 } } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 70 } } \right ) } { 7 \times 5 } - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { \sqrt{ \color{#FF6800}{ 7 } } \left ( \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 14 } } \right ) + \sqrt{ 7 } \left ( 3 \sqrt{ 70 } \right ) } { 7 \times 5 } - \sqrt{ 2 }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 14 } } + \sqrt{ 7 } \left ( 3 \sqrt{ 70 } \right ) } { 7 \times 5 } - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 14 } } + \sqrt{ 7 } \left ( 3 \sqrt{ 70 } \right ) } { 7 \times 5 } - \sqrt{ 2 }$
$ $ Simplify the expression $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { \color{#FF6800}{ 35 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 7 } \left ( 3 \sqrt{ 70 } \right ) } { 7 \times 5 } - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { 35 \sqrt{ 2 } + \sqrt{ \color{#FF6800}{ 7 } } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 70 } } \right ) } { 7 \times 5 } - \sqrt{ 2 }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { 35 \sqrt{ 2 } + \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 70 } } } { 7 \times 5 } - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { 35 \sqrt{ 2 } + \sqrt{ \color{#FF6800}{ 7 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 70 } } } { 7 \times 5 } - \sqrt{ 2 }$
$ $ Simplify the expression $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \dfrac { 35 \sqrt{ 2 } + \color{#FF6800}{ 21 } \sqrt{ \color{#FF6800}{ 10 } } } { 7 \times 5 } - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 35 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 21 } \sqrt{ \color{#FF6800}{ 10 } } } { \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } } - \sqrt{ 2 }$
$ $ Reduce the fraction $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } - 2 + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 10 } } } { \color{#FF6800}{ 5 } } } - \sqrt{ 2 }$
$\dfrac { 2 \sqrt{ 10 } } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 10 } } } { \color{#FF6800}{ 5 } } } - \sqrt{ 2 }$
$ $ Get the subtract $ $
$\dfrac { 2 \sqrt{ 10 } } { 5 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 10 } } } { \color{#FF6800}{ 5 } } } - \sqrt{ 2 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } } } { \color{#FF6800}{ 5 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 10 } } } { \color{#FF6800}{ 5 } } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } }$
$ $ Find the sum of the fractions $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 5 } } }$
$\dfrac { 2 \sqrt{ 10 } - 10 \color{#FF6800}{ + } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } + 3 \sqrt{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 2 } } } { 5 }$
$ $ Eliminate opponent number $ $
$\dfrac { 2 \sqrt{ 10 } - 10 + 3 \sqrt{ 10 } } { 5 }$
$\dfrac { \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 10 } } - 10 \color{#FF6800}{ + } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 10 } } } { 5 }$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 10 } } - 10 } { 5 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { \color{#FF6800}{ 5 } } }$
$ $ Reduce the fraction $ $
$\sqrt{ \color{#FF6800}{ 10 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
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