# Calculator search results

Formula
Calculate the value
$\dfrac{ 3- \sqrt{ 8 } }{ 3+ \sqrt{ 8 } } + \dfrac{ 3+ \sqrt{ 8 } }{ 3- \sqrt{ 8 } }$
$34$
Calculate the value
$\dfrac { 3 - \sqrt{ \color{#FF6800}{ 8 } } } { 3 + \sqrt{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$\dfrac { 3 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 3 + \sqrt{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 3 + \sqrt{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Get rid of unnecessary parentheses 
$\dfrac { 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 3 + \sqrt{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 - 2 \sqrt{ 2 } } { 3 + \sqrt{ \color{#FF6800}{ 8 } } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$\dfrac { 3 - 2 \sqrt{ 2 } } { 3 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 - 2 \sqrt{ 2 } } { 3 + 2 \sqrt{ 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Find the conjugate irrational number of denominator 
$\color{#FF6800}{ \dfrac { 3 - 2 \sqrt{ 2 } } { 3 + 2 \sqrt{ 2 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 3 - \left ( 2 \sqrt{ 2 } \right ) } { 3 - \left ( 2 \sqrt{ 2 } \right ) } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 - 2 \sqrt{ 2 } } { 3 + 2 \sqrt{ 2 } } \times \dfrac { 3 - \left ( 2 \sqrt{ 2 } \right ) } { 3 - \left ( 2 \sqrt{ 2 } \right ) } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 The denominator is multiplied by denominator, and the numerator is multiplied by numerator 
$\color{#FF6800}{ \dfrac { \left ( 3 - 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( 2 \sqrt{ 2 } \right ) \right ) } { \left ( 3 + 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( 2 \sqrt{ 2 } \right ) \right ) } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { \left ( 3 + 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( 2 \sqrt{ 2 } \right ) \right ) } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Expand using $\left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { \left ( 3 + 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( 2 \sqrt{ 2 } \right ) \right ) } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } - \left ( 2 \sqrt{ 2 } \right ) ^ { 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Calculate power 
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { \color{#FF6800}{ 9 } - \left ( 2 \sqrt{ 2 } \right ) ^ { 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Calculate power 
$\dfrac { 3 \times 3 + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - \color{#FF6800}{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Multiply $3$ and $3$
$\dfrac { \color{#FF6800}{ 9 } + 3 \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 + 3 \times \left ( \color{#FF6800}{ - } \left ( 2 \sqrt{ 2 } \right ) \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Move the (-) sign forward 
$\dfrac { 9 \color{#FF6800}{ - } 3 \left ( 2 \sqrt{ 2 } \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Get rid of unnecessary parentheses 
$\dfrac { 9 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Simplify the expression 
$\dfrac { 9 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 2 } \right ) \times 3 + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Get rid of unnecessary parentheses 
$\dfrac { 9 - 6 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Simplify the expression 
$\dfrac { 9 - 6 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( - 2 \sqrt{ 2 } \right ) \times \left ( - \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Get rid of unnecessary parentheses 
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } \color{#FF6800}{ - } 2 \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \left ( 2 \sqrt{ 2 } \right ) \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Since negative numbers are multiplied by an even number, remove the (-) sign 
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + 2 \sqrt{ 2 } \left ( 2 \sqrt{ 2 } \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Get rid of unnecessary parentheses 
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Simplify the expression 
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \color{#FF6800}{ 8 } } { 9 - 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Subtract $8$ from $9$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 1 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\dfrac { 9 - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 1 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 If the denominator is 1, the denominator can be removed 
$\color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$\color{#FF6800}{ 9 } - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \color{#FF6800}{ 8 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Add $9$ and $8$
$\color{#FF6800}{ 17 } - 6 \sqrt{ 2 } - 6 \sqrt{ 2 } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$17 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
 Calculate between similar terms 
$17 \color{#FF6800}{ - } \color{#FF6800}{ 12 } \sqrt{ \color{#FF6800}{ 2 } } + \dfrac { 3 + \sqrt{ 8 } } { 3 - \sqrt{ 8 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + \sqrt{ \color{#FF6800}{ 8 } } } { 3 - \sqrt{ 8 } }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 3 - \sqrt{ 8 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 - \sqrt{ \color{#FF6800}{ 8 } } }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) }$
 Get rid of unnecessary parentheses 
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 - 2 \sqrt{ 2 } }$
 Find the conjugate irrational number of denominator 
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ \dfrac { 3 + 2 \sqrt{ 2 } } { 3 - 2 \sqrt{ 2 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 3 - \left ( - 2 \sqrt{ 2 } \right ) } { 3 - \left ( - 2 \sqrt{ 2 } \right ) } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 + 2 \sqrt{ 2 } } { 3 - 2 \sqrt{ 2 } } \times \dfrac { 3 - \left ( - 2 \sqrt{ 2 } \right ) } { 3 - \left ( - 2 \sqrt{ 2 } \right ) }$
 The denominator is multiplied by denominator, and the numerator is multiplied by numerator 
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ \dfrac { \left ( 3 + 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( - 2 \sqrt{ 2 } \right ) \right ) } { \left ( 3 - 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( - 2 \sqrt{ 2 } \right ) \right ) } }$
$17 - 12 \sqrt{ 2 } + \dfrac { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) } { \left ( 3 - 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( - 2 \sqrt{ 2 } \right ) \right ) }$
 Expand using $\left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$17 - 12 \sqrt{ 2 } + \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { \left ( 3 - 2 \sqrt{ 2 } \right ) \left ( 3 - \left ( - 2 \sqrt{ 2 } \right ) \right ) }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \right ) }$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } - \left ( 2 \sqrt{ 2 } \right ) ^ { 2 } }$
 Calculate power 
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { \color{#FF6800}{ 9 } - \left ( 2 \sqrt{ 2 } \right ) ^ { 2 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
 Calculate power 
$17 - 12 \sqrt{ 2 } + \dfrac { 3 \times 3 + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - \color{#FF6800}{ 8 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
 Multiply $3$ and $3$
$17 - 12 \sqrt{ 2 } + \dfrac { \color{#FF6800}{ 9 } + 3 \times 2 \sqrt{ 2 } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
 Simplify the expression 
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( 2 \sqrt{ 2 } \right ) \times 3 + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
 Get rid of unnecessary parentheses 
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
 Simplify the expression 
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \left ( 2 \sqrt{ 2 } \right ) \times 2 \sqrt{ 2 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 }$
 Get rid of unnecessary parentheses 
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } } { 9 - 8 }$
 Simplify the expression 
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \color{#FF6800}{ 8 } } { 9 - 8 }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } }$
 Subtract $8$ from $9$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 1 } }$
$17 - 12 \sqrt{ 2 } + \dfrac { 9 + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + 8 } { \color{#FF6800}{ 1 } }$
 If the denominator is 1, the denominator can be removed 
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ 9 } + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 8 }$
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ 9 } + 6 \sqrt{ 2 } + 6 \sqrt{ 2 } + \color{#FF6800}{ 8 }$
 Add $9$ and $8$
$17 - 12 \sqrt{ 2 } + \color{#FF6800}{ 17 } + 6 \sqrt{ 2 } + 6 \sqrt{ 2 }$
$17 - 12 \sqrt{ 2 } + 17 + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } + \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } }$
 Calculate between similar terms 
$17 - 12 \sqrt{ 2 } + 17 + \color{#FF6800}{ 12 } \sqrt{ \color{#FF6800}{ 2 } }$
$17 \color{#FF6800}{ - } \color{#FF6800}{ 12 } \sqrt{ \color{#FF6800}{ 2 } } + 17 \color{#FF6800}{ + } \color{#FF6800}{ 12 } \sqrt{ \color{#FF6800}{ 2 } }$
 Eliminate opponent number 
$17 + 17$
$\color{#FF6800}{ 17 } \color{#FF6800}{ + } \color{#FF6800}{ 17 }$
 Add $17$ and $17$
$\color{#FF6800}{ 34 }$
Have you found the solution you wanted?
Try again
Try more features at QANDA!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture