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$6-3 \sqrt{ 5 } + \dfrac{ 1 }{ 6-3 \sqrt{ 5 } }$
$\dfrac { 16 - 10 \sqrt{ 5 } } { 3 }$
Calculate the value
$6 - 3 \sqrt{ 5 } + \dfrac { 1 } { 6 - 3 \sqrt{ 5 } }$
$ $ Find the conjugate irrational number of denominator $ $
$6 - 3 \sqrt{ 5 } + \color{#FF6800}{ \dfrac { 1 } { 6 - 3 \sqrt{ 5 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { 6 - \left ( - 3 \sqrt{ 5 } \right ) } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 1 } { 6 - 3 \sqrt{ 5 } } \times \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { 6 - \left ( - 3 \sqrt{ 5 } \right ) }$
$ $ The denominator is multiplied by denominator, and the numerator is multiplied by numerator $ $
$6 - 3 \sqrt{ 5 } + \color{#FF6800}{ \dfrac { 1 \left ( 6 - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \left ( 6 - 3 \sqrt{ 5 } \right ) \left ( 6 - \left ( - 3 \sqrt{ 5 } \right ) \right ) } }$
$6 - 3 \sqrt{ 5 } + \dfrac { \color{#FF6800}{ 1 } \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \right ) } { \left ( 6 - 3 \sqrt{ 5 } \right ) \left ( 6 - \left ( - 3 \sqrt{ 5 } \right ) \right ) }$
$ $ Multiply each term in parentheses by $ 1$
$6 - 3 \sqrt{ 5 } + \dfrac { \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \right ) } { \left ( 6 - 3 \sqrt{ 5 } \right ) \left ( 6 - \left ( - 3 \sqrt{ 5 } \right ) \right ) }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) \right ) }$
$ $ Expand the expression using $ \left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \color{#FF6800}{ 6 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \color{#FF6800}{ 6 } ^ { \color{#FF6800}{ 2 } } - \left ( 3 \sqrt{ 5 } \right ) ^ { 2 } }$
$ $ Calculate power $ $
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { \color{#FF6800}{ 36 } - \left ( 3 \sqrt{ 5 } \right ) ^ { 2 } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { 36 - \left ( \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } } \right ) ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 1 \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { 36 - \color{#FF6800}{ 45 } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + \color{#FF6800}{ 1 } \times \left ( - \left ( - 3 \sqrt{ 5 } \right ) \right ) } { 36 - 45 }$
$ $ Multiplying any number by 1 does not change the value $ $
$6 - 3 \sqrt{ 5 } + \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { 36 - 45 }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { \color{#FF6800}{ 36 } \color{#FF6800}{ - } \color{#FF6800}{ 45 } }$
$ $ Subtract $ 45 $ from $ 36$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 - \left ( - 3 \sqrt{ 5 } \right ) } { \color{#FF6800}{ - } \color{#FF6800}{ 9 } }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 3 \sqrt{ 5 } \right ) } { - 9 }$
$ $ Simplify Minus $ $
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 3 \sqrt{ 5 } } { - 9 }$
$6 - 3 \sqrt{ 5 } + \dfrac { 6 + 3 \sqrt{ 5 } } { \color{#FF6800}{ - } \color{#FF6800}{ 9 } }$
$ $ Move the minus sign to the front of the fraction $ $
$6 - 3 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 6 + 3 \sqrt{ 5 } } { 9 } }$
$6 - 3 \sqrt{ 5 } - \color{#FF6800}{ \dfrac { 6 + 3 \sqrt{ 5 } } { 9 } }$
$ $ Reduce the fraction $ $
$6 - 3 \sqrt{ 5 } - \color{#FF6800}{ \dfrac { 2 + \sqrt{ 5 } } { 3 } }$
$\color{#FF6800}{ 6 } - 3 \sqrt{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 + \sqrt{ 5 } } { 3 } }$
$ $ Find the sum of the fractions $ $
$\color{#FF6800}{ \dfrac { 18 - \left ( 2 + \sqrt{ 5 } \right ) } { 3 } } - 3 \sqrt{ 5 }$
$\dfrac { 18 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \right ) } { 3 } - 3 \sqrt{ 5 }$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$\dfrac { 18 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } } { 3 } - 3 \sqrt{ 5 }$
$\dfrac { \color{#FF6800}{ 18 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } - \sqrt{ 5 } } { 3 } - 3 \sqrt{ 5 }$
$ $ Subtract $ 2 $ from $ 18$
$\dfrac { \color{#FF6800}{ 16 } - \sqrt{ 5 } } { 3 } - 3 \sqrt{ 5 }$
$\color{#FF6800}{ \dfrac { 16 - \sqrt{ 5 } } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 5 } }$
$ $ Find the sum of the fractions $ $
$\color{#FF6800}{ \dfrac { 16 - \sqrt{ 5 } - 9 \sqrt{ 5 } } { 3 } }$
$\dfrac { 16 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 9 } \sqrt{ \color{#FF6800}{ 5 } } } { 3 }$
$ $ Calculate between similar terms $ $
$\dfrac { 16 \color{#FF6800}{ - } \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 5 } } } { 3 }$
Solution search results
search-thumbnail-Question $4$ 
If $x$ is $6$ what $|s$ 
$\dfrac {1} {3}x$ 
$1frac\left(1\right)\left(3\right)x$
1st-6th grade
Other
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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