Question

2/root3-5 rationalize the denominator

Answer 1

Given equation

$\dfrac{2}{\sqrt{3}-5 }$

Rationalizing, we get,

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

$= \dfrac{2\sqrt{3} +10}{(\sqrt{3})^{2} - 5^{2} }$

$= \dfrac{2\sqrt{3}+10 }{3-25}$

$= \dfrac{2\sqrt{3}+10 }{-22}$

$= \dfrac{2(\sqrt{3}+5) }{-22}$

$= \boxed{\boxed{\bold{\dfrac{\sqrt{3}+5 }{-11}}}}}$