Question

Rationalize the denominator of the following:

2
__________
√3-√5

Answer 1

Given :-

$\sf \bullet \;\; \dfrac{2}{\sqrt{3} - \sqrt{5}}$

To Do :-

• Rationalize the denominator

Solution :-

$\sf : \; \implies \dfrac{2}{\sqrt{3} -\sqrt{5} }$

$\sf : \; \implies \dfrac{2}{\sqrt{3} -\sqrt{5} } \times \dfrac{\sqrt{3} + \sqrt{5} }{\sqrt{3}+ \sqrt{5} }$

$\sf : \; \implies \dfrac{2 \times ( \sqrt{3} + \sqrt{5} )}{(\sqrt{3} -\sqrt{5}) \times (\sqrt{3} +\sqrt{5}) }$

$\sf : \; \implies \dfrac{2 \times (\sqrt{3}+ \sqrt{5} )}{(\sqrt{3})^{2} -(\sqrt{5})^{2} }$

$\sf : \; \implies \dfrac{2 \times ( \sqrt{3} +\sqrt{5} )}{ 3-5 }$

$\sf : \; \implies \dfrac{2 \times ( \sqrt{3} +\sqrt{5} )}{ -2 }$

$\sf : \; \implies - ( \sqrt{3} +\sqrt{5} \; )$

$\boxed{\bf{ \star \;\; \sqrt{3} -\sqrt{5}}}$