Insert a rational and an irrational number between 2 and 3. - Mathematics

Sum

Insert a rational and an irrational number between 2 and 3.

Solution

If a and b are two positive rational numbers such that ab is not a perfect square of a rational number, then sqrt(ab) is an irrational number lying between a and b.

Also, if a,b are rational numbers, then (a+b)/2 is a rational number between them.
∴ A rational number between 2 and 3 is (2+3)/2 = 2.5

An irrational number between 2 and 3 is = sqrt(2xx3)=sqrt6

Concept: Proofs of Irrationality
Is there an error in this question or solution?