Which of the following is a rational number?

Correct option is D

Given:

We need to identify which of the following is a rational number.

Concept Used:

A rational number has the form $$\frac{p}{q}$$​, where p and q are integers and $$q \neq 0$$​.

Solution:

Option A: $$(\sqrt{2} + \sqrt{5})^2$$​ is irrational because the square of an irrational sum is still irrational.

Option B: $$2 + \sqrt{5}$$​ is irrational because $$\sqrt{5}$$​ is irrational.

Option C: $$2 - \sqrt{5}$$​ is irrational because$$\sqrt{5}$$​ is irrational.

Option D: $$(\sqrt{2} + \frac{1}{\sqrt{8}})^2$$​

​$$2 + \frac{1}{8} + 2 \times \sqrt{2} \times \frac{1}{\sqrt 8}= \frac{25}{8}$$​​

Thus, the rational number is Option D.