Question

Rationalize:-

$\frac{2}{√5- √3}$​

Answer 1

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Answer 2

★FIND:

Rationalization of $\frac{2}{ \sqrt{5} - \sqrt{3} }$

★GIVEN,

➡️ $\frac{2}{ \sqrt{5} - \sqrt{3} }$

➡️SOLUTION:

$= > \frac{2}{ \sqrt{5} - \sqrt{3} } \\ = > \frac{2}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ = > \frac{2( \sqrt{5} + \sqrt{3} ) }{( \sqrt{5) {}^{2}} - ( \sqrt{3) {}^{2} } } (since \: (a {}^{2} - b {}^{2} ) = (a + b)(a - b) \\ = > \frac{2( \sqrt{5} + \sqrt{3})}{(5) - (3)} \\ = > \frac{2( \sqrt{5} + \sqrt{3} )}{2} \\ = > \sqrt{5} + \sqrt{3}$