Some perfect squares (such as 100), have a digit sum (1+0+0=1) that is equal to the digit sum of their square root (1+0=1). Some other perfect squares (such as 121), have a digit sum (1+2+1=4) that is equal to the square of the digit sum of their square root ((1+1)2=4). What is the smallest perfect square greater than 100 that is in both of these two categories?
