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$\dfrac{ 3 }{ 2 \sqrt{ 3 } -3 }$
$2 \sqrt{ 3 } + 3$
Calculate the value
$\dfrac { 3 } { 2 \sqrt{ 3 } - 3 }$
$ $ Find the conjugate irrational number of denominator $ $
$\color{#FF6800}{ \dfrac { 3 } { 2 \sqrt{ 3 } - 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 2 \sqrt{ 3 } + 3 } { 2 \sqrt{ 3 } + 3 } }$
$\dfrac { 3 } { 2 \sqrt{ 3 } - 3 } \times \dfrac { 2 \sqrt{ 3 } + 3 } { 2 \sqrt{ 3 } + 3 }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$\color{#FF6800}{ \dfrac { 3 \left ( 2 \sqrt{ 3 } + 3 \right ) } { \left ( 2 \sqrt{ 3 } - 3 \right ) \left ( 2 \sqrt{ 3 } + 3 \right ) } }$
$\dfrac { \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) } { \left ( 2 \sqrt{ 3 } - 3 \right ) \left ( 2 \sqrt{ 3 } + 3 \right ) }$
$ $ Multiply each term in parentheses by $ 3$
$\dfrac { \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } { \left ( 2 \sqrt{ 3 } - 3 \right ) \left ( 2 \sqrt{ 3 } + 3 \right ) }$
$\dfrac { 3 \left ( 2 \sqrt{ 3 } \right ) + 3 \times 3 } { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$\dfrac { 3 \left ( 2 \sqrt{ 3 } \right ) + 3 \times 3 } { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } }$
$\dfrac { 3 \left ( 2 \sqrt{ 3 } \right ) + 3 \times 3 } { \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } - 3 ^ { 2 } }$
$ $ Calculate power $ $
$\dfrac { 3 \left ( 2 \sqrt{ 3 } \right ) + 3 \times 3 } { \color{#FF6800}{ 12 } - 3 ^ { 2 } }$
$\dfrac { 3 \left ( 2 \sqrt{ 3 } \right ) + 3 \times 3 } { 12 - \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$\dfrac { 3 \left ( 2 \sqrt{ 3 } \right ) + 3 \times 3 } { 12 - \color{#FF6800}{ 9 } }$
$\dfrac { \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \right ) + 3 \times 3 } { 12 - 9 }$
$ $ Get rid of unnecessary parentheses $ $
$\dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + 3 \times 3 } { 12 - 9 }$
$\dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } + 3 \times 3 } { 12 - 9 }$
$ $ Simplify the expression $ $
$\dfrac { \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 3 } } + 3 \times 3 } { 12 - 9 }$
$\dfrac { 6 \sqrt{ 3 } + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } { 12 - 9 }$
$ $ Multiply $ 3 $ and $ 3$
$\dfrac { 6 \sqrt{ 3 } + \color{#FF6800}{ 9 } } { 12 - 9 }$
$\dfrac { 6 \sqrt{ 3 } + 9 } { \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 9 } }$
$ $ Subtract $ 9 $ from $ 12$
$\dfrac { 6 \sqrt{ 3 } + 9 } { \color{#FF6800}{ 3 } }$
$\color{#FF6800}{ \dfrac { 6 \sqrt{ 3 } + 9 } { 3 } }$
$ $ Reduce the fraction $ $
$\color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
Solution search results
search-thumbnail-$11.$ Question $11$ 
Solve the $:$ $folloMlng'$ $0<θ<90^{°}$ 
$\left(1\right)$ $2sin^{2}θ=1\right)$ $\left(rac\left(3\right)\left(2\right)\right)$ 
$\left(11\right)$ $3tan^{2}θ+2=3$ 
$\left(111\right)cos^{2}θ$ $11rac\left(1\right)\left(4\right)\right)=$ 
$c\left(1\right)\left(4\right)\right)=11113c\left(1\right)\left(2\right)\right)$
10th-13th grade
Trigonometry
search-thumbnail-Which of the following rational numbers are 
equivalent? 
$0Ptionsy$ 
A \frac{5}{6}, \frac{30}{36} 
B $s\sqrt{rac\left(} -2\right)\left(3\right)\sqrt{1rac} \sqrt{4\right)16\right)4} $ 
C $s\sqrt{11aC\left(} -4\right)1-7b,\sqrt{1rac\left(16\sqrt{35\right)9} } $ 
D \frac{1}{2},\frac{3}{8}
7th-9th grade
Other
search-thumbnail-The rationalizing factor of \sqrt{23} is 
$°$ $Options^{°}$ $0$ 
A 24 
23 
C \sqrt{23} 
D None of these
7th-9th grade
Other
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