# Calculator search results

Formula
Calculate the value
$\dfrac{ \sqrt{ 6 } +3 \sqrt{ 2 } }{ \sqrt{ 3 } } + \dfrac{ 3 \sqrt{ 2 } }{ \sqrt{ 6 } + \sqrt{ 3 } }$
$\sqrt{ 2 } + 2 \sqrt{ 3 }$
Calculate the value
$\color{#FF6800}{ \dfrac { \sqrt{ 6 } + 3 \sqrt{ 2 } } { \sqrt{ 3 } } } + \dfrac { 3 \sqrt{ 2 } } { \sqrt{ 6 } + \sqrt{ 3 } }$
 Calculate the expression 
$\color{#FF6800}{ \dfrac { 3 \sqrt{ 2 } + 3 \sqrt{ 6 } } { 3 } } + \dfrac { 3 \sqrt{ 2 } } { \sqrt{ 6 } + \sqrt{ 3 } }$
$\color{#FF6800}{ \dfrac { 3 \sqrt{ 2 } + 3 \sqrt{ 6 } } { 3 } } + \dfrac { 3 \sqrt{ 2 } } { \sqrt{ 6 } + \sqrt{ 3 } }$
 Reduce the fraction 
$\sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ \color{#FF6800}{ 6 } } + \dfrac { 3 \sqrt{ 2 } } { \sqrt{ 6 } + \sqrt{ 3 } }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { 3 \sqrt{ 2 } } { \sqrt{ 6 } + \sqrt{ 3 } }$
 Find the conjugate irrational number of denominator 
$\sqrt{ 2 } + \sqrt{ 6 } + \color{#FF6800}{ \dfrac { 3 \sqrt{ 2 } } { \sqrt{ 6 } + \sqrt{ 3 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 6 } - \sqrt{ 3 } } { \sqrt{ 6 } - \sqrt{ 3 } } }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { 3 \sqrt{ 2 } } { \sqrt{ 6 } + \sqrt{ 3 } } \times \dfrac { \sqrt{ 6 } - \sqrt{ 3 } } { \sqrt{ 6 } - \sqrt{ 3 } }$
 The denominator is multiplied by denominator, and the numerator is multiplied by numerator 
$\sqrt{ 2 } + \sqrt{ 6 } + \color{#FF6800}{ \dfrac { \left ( 3 \sqrt{ 2 } \right ) \left ( \sqrt{ 6 } - \sqrt{ 3 } \right ) } { \left ( \sqrt{ 6 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 6 } - \sqrt{ 3 } \right ) } }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \left ( \sqrt{ 6 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 6 } - \sqrt{ 3 } \right ) }$
 Multiply each term in parentheses by $3 \sqrt{ 2 }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { \left ( \sqrt{ 6 } + \sqrt{ 3 } \right ) \left ( \sqrt{ 6 } - \sqrt{ 3 } \right ) }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \left ( 3 \sqrt{ 2 } \right ) \sqrt{ 6 } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right ) \left ( \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) }$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \left ( 3 \sqrt{ 2 } \right ) \sqrt{ 6 } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \left ( 3 \sqrt{ 2 } \right ) \sqrt{ 6 } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { \left ( \sqrt{ \color{#FF6800}{ 6 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
 Calculate power 
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \left ( 3 \sqrt{ 2 } \right ) \sqrt{ 6 } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { \color{#FF6800}{ 6 } - \left ( \sqrt{ 3 } \right ) ^ { 2 } }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \left ( 3 \sqrt{ 2 } \right ) \sqrt{ 6 } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { 6 - \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
 Calculate power 
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \left ( 3 \sqrt{ 2 } \right ) \sqrt{ 6 } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { 6 - \color{#FF6800}{ 3 } }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \sqrt{ \color{#FF6800}{ 6 } } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { 6 - 3 }$
 Get rid of unnecessary parentheses 
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 6 } } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { 6 - 3 }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 6 } } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { 6 - 3 }$
 Simplify the expression 
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 3 } } + \left ( 3 \sqrt{ 2 } \right ) \times \left ( - \sqrt{ 3 } \right ) } { 6 - 3 }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { 6 \sqrt{ 3 } + \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { 6 - 3 }$
 Get rid of unnecessary parentheses 
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { 6 \sqrt{ 3 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { 6 - 3 }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { 6 \sqrt{ 3 } + \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) } { 6 - 3 }$
 Simplify the expression 
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { 6 \sqrt{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 6 } } } { 6 - 3 }$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { 6 \sqrt{ 3 } - 3 \sqrt{ 6 } } { \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } }$
 Subtract $3$ from $6$
$\sqrt{ 2 } + \sqrt{ 6 } + \dfrac { 6 \sqrt{ 3 } - 3 \sqrt{ 6 } } { \color{#FF6800}{ 3 } }$
$\sqrt{ 2 } + \sqrt{ 6 } + \color{#FF6800}{ \dfrac { 6 \sqrt{ 3 } - 3 \sqrt{ 6 } } { 3 } }$
 Reduce the fraction 
$\sqrt{ 2 } + \sqrt{ 6 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } }$
$\sqrt{ 2 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } } + 2 \sqrt{ 3 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } }$
 Remove the two numbers if the values are the same and the signs are different 
$\sqrt{ 2 } + 2 \sqrt{ 3 }$
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