Question

Rationalise denominator in
1÷root 2+root3​

Answer 1

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Answer 2

Answer:

$\boxed{\bold{\mathsf{= \sqrt{3} - \sqrt{2} }}}$

Step-by-step explanation:

Given,

On rationalizing the denominator as follows,

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

We get here $\boxed{\huge{\bold{\mathsf{= \sqrt{3} - \sqrt{2} }}}}$