Question

rationalize 2/root 2+root 3


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Answer 1

Answer:

$\frac{2}{ \sqrt{2} + \sqrt{3} } \\ = \frac{2}{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } \\ = \frac{2( \sqrt{2} - \sqrt{3)} }{ { \sqrt{2} }^{2} - { \sqrt{3} }^{2} } \\ = \frac{2( \sqrt{2} - \sqrt{3)} }{2 - 3} \\ = \frac{2( \sqrt{2} - \sqrt{3} }{ - 1} \\ = - 2( \sqrt{2} - \sqrt{3} )$

Answer 2

Answer:

$\huge\bold{\underline{\underline{Solution}}}$

$\implies \dfrac{2}{ \sqrt{2} + \sqrt{3} } \times \dfrac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3}} \\ \\ \\ \implies \frac{2( \sqrt{2} - \sqrt{3})}{{ (\sqrt{2} }^{2}) - ( { \sqrt{3} }^{2})} \\ \\ \\ \implies \frac{2( \sqrt{2} - \sqrt{3})}{2 - 3} \\ \\ \\ \implies \frac{2( \sqrt{2} - \sqrt{3})}{ - 1} \\ \\ \\ \implies - 2( \sqrt{2} - \sqrt{3} ) \\ \\ \\ \implies - 2 \sqrt{2} + 2 \sqrt{3}$