What is the height of the tv and is it square inches or inches ? ?

To find the height of the TV you first need to realize that the question is giving you dimensions for a triangle. 

Every triangle has a hypotenuse and two sides. To find the hypotenuse you square both sides, add them, and then square root. So to find one of the sides you get the hypotenuse, square it, and subtract the square length of the given side. 

The equation is 25^2-20^2.
Which if simplified is 625-400, the then solution is going to be 225. 
You next will square root 225, 225^(1/2). Which your answer should be 15 inches for the missing side length.

The answer is 15 inches.  Not squared.  You can use the Pythagorean theorem.   
Since the diagonal is 25, that is the hypotenuse, and the base, which is 20, is the bottom leg, then the missing side is the height.  
20^2 + b^2 = 25^2
400 + b^2 = 625
b^2 = sqrt(625-400)
b = sqrt 225
b=15