5. Rationalize the denominator of the following :
i)$$1/\sqrt{7}$$
ii)$$1/{\sqrt{7} - \sqrt{6}}$$
iii)$$1/{\sqrt{5} + \sqrt{2}}$$
iv)$$1/{\sqrt{7} - 2}$$

To rationalize the denominator, we need to multiply the irrational denominator by it's conjugate.
i) = $$1/\sqrt{7}$$ × $$\sqrt{7}/\sqrt{7}$$
= $$\sqrt{7}/7$$

ii) = $$1/(\sqrt{7} - \sqrt{6})$$ × $$(\sqrt{7} + \sqrt{6})/(\sqrt{7} + \sqrt{6})$$
= $$(\sqrt{7} + \sqrt{6})/(7-6)$$
= $${\sqrt{7} + \sqrt{6}}$$

iii) = $$1/(\sqrt{5} + \sqrt{2})$$ × $$(\sqrt{5} - \sqrt{2})/(\sqrt{5} - \sqrt{2})$$
$$= (\sqrt{5} - \sqrt{2})/(5 - 2)$$
= $$(\sqrt{5} - \sqrt{2})/3$$

iv) = $$1/(\sqrt{7} - 2)$$ × $$(\sqrt{7} + 2)/(\sqrt{7} + 2)$$
=$$(\sqrt{7} + 2)/(7 - 4)$$
=$${\sqrt{7} - 2}/3$$