Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Question

For real numbers \(x\) and \(y\), we define \(x R y\) iff \(x - y + \sqrt{5}\) is an irrational number. Then, relation \(R\) is:

Answer 1

If numbers such as\( \sqrt4 = 2, \sqrt9 = 3\) are considered, Then here, 2 and 3 are rational numbers.

Thus, the square roots of all positive integers are not irrational.

Solution and Explanation