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Calculate the value
Answer
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$\sqrt{ 2 } \left( \sqrt{ 2 } - \sqrt{ 3 } \right) + \sqrt{ 3 } \left( \sqrt{ 2 } + \sqrt{ 3 } \right)$
$5$
Calculate the value
$\sqrt{ \color{#FF6800}{ 2 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$ $ Multiply each term in parentheses by $ \sqrt{ 2 }$
$\sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\sqrt{ \color{#FF6800}{ 2 } } \sqrt{ 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\left ( \sqrt{ 2 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\left ( \sqrt{ 2 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$ $ Add the exponent as the base is the same $ $
$\left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$ $ Add $ 1 $ and $ 1$
$\left ( \sqrt{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$\left ( \sqrt{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$ $ If you square the radical sign, it will disappear $ $
$\color{#FF6800}{ 2 } + \sqrt{ 2 } \times \left ( - \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$2 + \sqrt{ 2 } \times \left ( \color{#FF6800}{ - } \sqrt{ 3 } \right ) + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$ $ Move the (-) sign forward $ $
$2 \color{#FF6800}{ - } \sqrt{ 2 } \sqrt{ 3 } + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$2 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \sqrt{ \color{#FF6800}{ 3 } } + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$ $ Calculate multiplication $ $
$2 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 3 } \left ( \sqrt{ 2 } + \sqrt{ 3 } \right )$
$2 - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 3 } } \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \right )$
$ $ Multiply each term in parentheses by $ \sqrt{ 3 }$
$2 - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 3 } }$
$2 - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ \color{#FF6800}{ 2 } } + \sqrt{ 3 } \sqrt{ 3 }$
$ $ Calculate multiplication of root $ $
$2 - \sqrt{ 6 } + \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 3 } \sqrt{ 3 }$
$2 \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 6 } } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 6 } } + \sqrt{ 3 } \sqrt{ 3 }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$2 + \sqrt{ 3 } \sqrt{ 3 }$
$2 + \sqrt{ \color{#FF6800}{ 3 } } \sqrt{ 3 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$2 + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 }$
$2 + \left ( \sqrt{ 3 } \right ) ^ { 1 } \sqrt{ \color{#FF6800}{ 3 } }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$2 + \left ( \sqrt{ 3 } \right ) ^ { 1 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } }$
$2 + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } } \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } }$
$ $ Add the exponent as the base is the same $ $
$2 + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$2 + \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$ $ Add $ 1 $ and $ 1$
$2 + \left ( \sqrt{ 3 } \right ) ^ { \color{#FF6800}{ 2 } }$
$2 + \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ If you square the radical sign, it will disappear $ $
$2 + \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$ $ Add $ 2 $ and $ 3$
$\color{#FF6800}{ 5 }$
Solution search results
search-thumbnail-$s|ef\left(-1n$ $\left($ }\right)^{50}\ $\right)$ \ | | is\ equal\ to\ $S$ 
$s1S$ 
$S-1S$ 
$s2S$ 
$s50s$
7th-9th grade
Other
search-thumbnail-$8 \times $ 
$ = $ In $ \dfrac { E } { 8 } $ $ \left. \begin{array} { l } { \dfrac { 1 } { 3 } } \\ { \dfrac { 11 } { 3 } } \end{array} \right. $ $ \left. \begin{array} { l } { \dfrac { 1 } { 1 } } \\ { \dfrac { 1 } { 1 } } \end{array} \right. $ and $ \left. \begin{array} { l } { δ } \\ { 8 } \end{array} \right. $ 
Find the length of PR. $ \bar { I } $ 
$0$ 
$ \bar { u } $ 
$2$ $ = $ $ \| = $
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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