Click on the video above to start the movie. Mr. Sobek will explain a short-cut math trick that will enable you to easily square whole numbers up to 99. After four examples he will explain why the trick works.
The same procedure can be applied to numbers larger than 99, but I would need to remove the word, "easily" from the title unless the number is close to a power of 10. For example, squaring 998 would still be easy by taking 1000 x 996 + 4.
The picture below provides a nice summary of the procedure.

Click the following link to go to a drill to practice squaring two digit numbers: Practice Drill