The number $$\frac{\sqrt{2} + \sqrt{7}}{\sqrt{2 - \sqrt{7}}}$$​is:

Correct option is A

Given:​

​$$\frac{\sqrt{2} + \sqrt{7}}{\sqrt{2 - \sqrt{7}}}$$

Concept Used:

An irrational number is a real number that cannot be expressed as a ratio of integers;

for example, $$\sqrt 2$$ is an irrational number. 

We cannot express any irrational number in the form of a ratio, such as $$\frac pq$$​, where p and q are integers, q≠0.

​Solution:

​$$\frac{\sqrt{2} + \sqrt{7}}{\sqrt{2 - \sqrt{7}}}$$​​

=$$\frac{\sqrt{2} + \sqrt{7}}{\sqrt{2 - \sqrt{7}}}\times\frac{\sqrt{2 - \sqrt{7}}}{\sqrt{2 - \sqrt{7}}}$$

=$$\frac{\sqrt{2} + \sqrt{7}\times \sqrt{2 - \sqrt{7}}}{2 - \sqrt{7}} \times \frac{2 +\sqrt{7}}{2 + \sqrt{7}}$$

=$$\frac{(\sqrt{2} + \sqrt{7})\times \sqrt{2 - \sqrt{7}}\times (2 +\sqrt{7})}{4 - 7}$$

=$$\frac{(\sqrt{2} + \sqrt{7})\times \sqrt{2 - \sqrt{7}}\times (2 +\sqrt{7})}{-3}$$

We can say that , above expression is an irrational number.