Doing Math In My Head

Just as I went to bed the other night, unbidden, I remembered reading that a few days ago, we had a date with a perfect square:  7-24-25.  At least I thought that was the date and set-about confirming it in my head.  7 x 7 = 49 was easy.  Next up was 25 x 25.  I figured 4 x 25 =100 and 4 goes into 25, 6 times with a remainder of 1, so 625.  I could do 24 x 24 the same way, but it would be 6 x (100 -4), which would be 600-24, so I'm missing 24 and the remainder of 25 for a total of 49.