Rationalize \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} – \sqrt{3}}\)
-
\(-5 - 2\sqrt{6}\)
- \(-5 + 3\sqrt{2}\)
- \(5 - 2\sqrt{3}\)
- \(5 + 2\sqrt{6}\)
The correct answer is: A
Explanation
\(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)
= \((\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}})(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}})\)
= \(\frac{2 + \sqrt{6} + \sqrt{6} + 3}{2 - \sqrt{6} + \sqrt{6} - 3}\)
= \(\frac{5 + 2\sqrt{6}}{-1}\)
= \(- 5 - 2\sqrt{6}\)
There is an explanation video available .