Question

Rationalise the denominator
$\boxed{\tt \dfrac{5}{ \sqrt{21} - 9}}$
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Answer 1

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$\large \pmb{\sf{Question :-}}$

$\textsf{Rationalise the denominator : }{\tt \dfrac{5}{ \sqrt{21} - 9}}$

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$\large \pmb{\sf{Final \: Answer:-}}$

$\purple {\bigstar } \color{maroon} \boxed{\sf \color{green}{ : \leadsto \frac{-5\sqrt{21}-45}{60}}}$

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$\large \pmb{\sf{Step-by-step \: Solution :-}}$

$\sf : \leadsto \frac{5}{ \sqrt{21} - 9}$

$\sf : \leadsto \frac{5}{ \sqrt{21} - 9} \: \times \frac{ \sqrt{21} + 9 }{ \sqrt{21} + 9 }$

$\footnotesize \color{green} \boxed { \textsf \color{purple}{Rationalizing the denominator }}$

$\sf : \leadsto \frac{5(\sqrt{21} + 9 )}{( \sqrt{21} - 9)(\sqrt{21} + 9 )}$

$\sf : \leadsto \frac{5(\sqrt{21} + 9 )}{21 - 81}$

$\sf : \leadsto \frac{5(\sqrt{21} + 9 )}{ - 60}$

$\pink \bigstar \: \sf : \leadsto \frac{ - 5\sqrt{21} - 45}{ 60}$

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$\sf \color{azure}\fcolorbox{pink}{purple}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \#Bebrainly \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\:\: \: \: \: \:}$

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$\sf \color{azure}\fcolorbox{pink}{black}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: @Saanvigrover2007 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}$

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Answer 2

TO FIND :-

$\red{\tt \dfrac{5}{ \sqrt{21} - 9}}$

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SOLUTION :-

$\large\red\Longrightarrow \bold \red{ \frac{5}{ \sqrt{21 - 9}} } \red\times \frac \red{ \sqrt{21 } + 9} \red{ \sqrt{21} + 9 }$

$\large \red\Longrightarrow \red{ \frac{5( \sqrt{21 + 9)} }{ \sqrt{21 - 9) \times (\sqrt{21 + 9)} } } }$

$\large \red\Longrightarrow \red{ \frac{5( \sqrt{21 } + 9)}{21 - 81}}$

$\large \red\Longrightarrow \red{ \frac{5( \sqrt{21} + 9)}{ - 60}}$

$\large \red\Longrightarrow \red{ \frac{ \sqrt{21} + 9}{ - 12}}$

FINAL ANSWER :-

$\huge \red\Longrightarrow \red{ - \frac{ \sqrt{21} + 9}{12}}$

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ALTERNATE FORM :-

1.13188

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