Rationalize the expression \(\frac{1}{\sqrt{2} + \sqrt{5}}\)
A
\(\frac{1}{3}\)(\(\sqrt{5} - \sqrt{2}\)
B
\(\frac{\sqrt{2}}{3}\) + \(\frac{\sqrt{5}}{5}\)
C
\(\sqrt{2} - \sqrt{5}\)
D
5(\(\sqrt{2} - \sqrt{5}\)
E
\(\frac{1}{3}\)(\(\sqrt{2} - \sqrt{5}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{1}{\sqrt{2} + \sqrt{5}}\)
\(\frac{1}{\sqrt{2} + \sqrt{5}} \times \frac{(\sqrt{2} - \sqrt{5})}{(\sqrt{2} - \sqrt{5})}\)
= \(\frac{\sqrt{2} - \sqrt{5}}{2 - 5}\)
= \(\frac{\sqrt{2} - \sqrt{5}}{-3}\)
= \(\frac{1}{3} (\sqrt{5} - \sqrt{2})\)
Source: Myschool Past Questions Archive (Record #32481)