Question

Rationalize the denominator:
10
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√10−√5

Answer 1

Answer:

$\frac{10}{ \sqrt{10} - \sqrt{5} } \\ multiply \: by \: \frac{ \sqrt{10} + \sqrt{5} }{ \sqrt{10} + \sqrt{5} } \\ = \frac{10}{ \sqrt{10} - \sqrt{5} } \times \frac{ \sqrt{10} + \sqrt{5} }{ \sqrt{10} + \sqrt{5} } \\ = \frac{10 \sqrt{10} + 10 \sqrt{5} }{ (\sqrt{10}) {}^{2} - ( \sqrt{5} ) {}^{2} } \\ = \frac{10 \sqrt{10} + 10 \sqrt{5} }{10 - 5} \\ = \frac{10 \sqrt{10} + 10 \sqrt{5} }{5} \\ = \frac{5(2 \sqrt{10} + 2 \sqrt{5}) }{5} \\ = (2 \sqrt{10} + 2 \sqrt{5} ) \: \: ans$

Answer 2

${\huge{\bold{\pink{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

Rationalize the Denominator

$\sf\dfrac{10}{\sqrt 10 - \sqrt 5}$

${\huge{\bold{\pink{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

$\sf\implies\dfrac{10}{\sqrt 10 - \sqrt 5}$

$\sf\implies\dfrac{10}{\sqrt 10 - \sqrt 5}\times\dfrac{\sqrt 10 + \sqrt 5}{\sqrt 10 + sqrt 5}$

${\bold{\blue{\boxed{\bf{(a+b) (a-b) = a^2 - b^2 }}}}}$

$\sf\implies\dfrac{10(\sqrt 10 + \sqrt 5)}{\sqrt 10^2 - \sqrt 5^2}$

$\sf\implies\dfrac{10(\sqrt 10 + \sqrt 5)}{ 10 - 5}$

$\sf\implies\dfrac{\cancel 10(\sqrt 10 + \sqrt 5)}{\cancel 5}$

$\sf\implies 2(\sqrt 10 + \sqrt 5)$

${\bold{\blue{\boxed{\bf{2(\sqrt 10 + \sqrt 5)}}}}}$

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