Alien Challenge: Save the Earth!!!!

An energy being from Alpha Centauri comes to your home to test Humanities intelligence.  IF you answer correctly, humanity will become part of a large intergalactic federation. If you answer incorrectly, the alien will shroud the Earth in perpetual darkness.  Here's the problem:

1.  Consider an integer N that is greater than 1.

2.  Consider the integer M, which is the square root of N.

3.  Given that M is the sum the digits of N, what is N and M?

Hint:  Only one value of N can satisfy these properties.