When the tangent of the intersection p is parallel to the straight line y=x-2,

The distance from point P to line y=x-2 is the smallest.

The slope of the straight line y=x-2 is equal to 1,

Let y=x2-lnx = 2x-= 1, x= 1, or x=- 1/2 (omitted).

Therefore, the tangent coordinates (1, 1) on the curve y=x2-lnx parallel to the straight line y=x-2,

The distance from the point (1, 1) to the straight line y=x-2 is equal to √2.

So the minimum distance from point P to line y=x-2 is √2.

So the answer is √2.

This topic examines the application of the distance formula from a point to a straight line, the solution of the derivative of the function and the significance of the derivative, which embodies the mathematical thought of reduction.