Math, asked by shamik1302, 10 months ago

Rationalize the denominator:
10
-------------
√10−√5

Answers

Answered by 007Boy
2

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

Answered by InfiniteSoul
1

{\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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