Squaring numbers between 60 & 40

Here's a quick way to square numbers between 40 and 60. You know the squares of 40, 50, and 60, right?

So let's show what to do for N=51 through 59. Write N as (50+R) for R between 1 and 9. Then N² will have first two digits (25+R) and last two digits R². Thus:

52²= 2704,

58²= 3364,

since 27=25+2 and 33=25+8.

The rule for N=41 through 49 is similar. Write N as (40+R) for R between 1 and 9. Then N² will have first two digits (15+R) and last two digits (10-R)². So:

42²= 1764.

48²= 2304.