Do you have enough information to work out the area of the shaded quadrilateral?

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

Prove that if a is a natural number and the square root of a is rational, then it is a square number (an integer n^2 for some integer n.)