Question

rationalise 2/root5+root3​

Answer 1

Answer:

The answer is $\sqrt 5-\sqrt 3$

Step-by-step explanation:

Given number is  $\dfrac{2}{\sqrt 5+\sqrt 3}$

Rationalize denominator  

              $=\dfrac{2}{\sqrt 5+\sqrt 3}\times \dfrac{\sqrt 5-\sqrt 3}{\sqrt 5-\sqrt 3}$

              $=\dfrac{2}{(\sqrt 5)^2-(\sqrt 3)^2}\times (\sqrt 5-\sqrt 3)$   Using $(a+b)(a-b)=a^2-b^2$

              $=\dfrac{2}{5-3}\times (\sqrt 5-\sqrt 3)\\\\=\dfrac{2}{2}\times (\sqrt 5-\sqrt 3)=\sqrt 5-\sqrt 3$