There is a two digit number with the unique property that if a decimal point is inserted between the two digits, the resulting number is the average of the square of the digits.

Part 2:

There is a four digit number with the unique property that if a decimal point is inserted between the first and second digits, the resulting number is the average of the square of the digits.

What are these averages? Report your answers with the decimal point appropriately positioned, and include any trailing zeros, if any, to clearly indicate the number of digits present.

Bonus: What about raising digits to integer powers higher than 2, different numbers of digits, and other locations of the decimal point? How many can you find?