Math, asked by grewal270599, 10 months ago

rationalize the denominator 1 by under root 5 + under root 2 and subtract it from under root 5 minus under root 2​

Answers

Answered by Anonymous
217

Answer:

\underline{\bigstar\:\textsf{Rationalization of Denominator :}}

:\implies\tt \dfrac{1}{ \sqrt{5} +  \sqrt{2} } -(\sqrt{5} -  \sqrt{2})\\\\\\:\implies\tt \bigg(\dfrac{1}{ \sqrt{5} + \sqrt{2} } \times\dfrac{\sqrt{5} -  \sqrt{2} }{ \sqrt{5} - \sqrt{2}} \bigg) -  \sqrt{5} + \sqrt{2}\\\\\\:\implies\tt  \dfrac{ \sqrt{5} - \sqrt{2} }{ {(\sqrt{5})}^{2} -{(\sqrt{2})}^{2}} -  \sqrt{5} + \sqrt{2}\\\\\\:\implies\tt  \dfrac{\sqrt{5} -\sqrt{2}}{5 - 2} -  \sqrt{5} + \sqrt{2}\\\\\\:\implies\tt  \dfrac{ \sqrt{5} - \sqrt{2} }{3} -  \sqrt{5} + \sqrt{2}\\\\\\:\implies\tt  \dfrac{ \sqrt{5} -  \sqrt{2} - 3 \sqrt{5} + 3 \sqrt{2} }{3}\\\\\\:\implies\tt  \dfrac{2\sqrt{2} - 2 \sqrt{5}}{3}\\\\\\:\implies\underline{\boxed{\red{\tt\dfrac{2( \sqrt{2} - \sqrt{5})}{3}}}}

Answered by sweetygupta14011884
0

Answer:

Rationalize the denomination and subtract

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