19. What is the greatest lower bound of the set of rational numbers whose squares are between 2 and 3?

 

A.

B.

C.

D.

E.

 

Solution: The answer is B

 

The set of rational numbers is defined as the set having elements of the form p/q where p and q are integers. If the squares of a rational number is between 2 and 3, that is, if

Then the set of rational numbers satisfies the following inequality,

 

 

Which implies that the greatest lower bound of the set of rational numbers whose squares are between 2 and 3 is the negative square root of 3.