Rationalize the expression \(\frac{1}{\sqrt{2} + \sqrt{5}...
Rationalize the expression \(\frac{1}{\sqrt{2} + \sqrt{5}}\)
\(\frac{1}{3}\)(\(\sqrt{5} - \sqrt{2}\)
\(\frac{\sqrt{2}}{3}\) + \(\frac{\sqrt{5}}{5}\)
\(\sqrt{2} - \sqrt{5}\)
5(\(\sqrt{2} - \sqrt{5}\)
\(\frac{1}{3}\)(\(\sqrt{2} - \sqrt{5}\)
Correct answer is A
\(\frac{1}{\sqrt{2} + \sqrt{5}}\)
\(\frac{1}{\sqrt{2} + \sqrt{5}} \times \frac{(\sqrt{2} - \sqrt{5})}{(\sqrt{2} - \sqrt{5})}\)
= \(\frac{\sqrt{2} - \sqrt{5}}{2 - 5}\)
= \(\frac{\sqrt{2} - \sqrt{5}}{-3}\)
= \(\frac{1}{3} (\sqrt{5} - \sqrt{2})\)