Method for [Mentally] Calculating Squares

Proposal

Let a and b be real numbers for which a² is readily known and b² has yet to be calculated. Also let h be "step size", and be equal to b - a. Then:

b² = a² + 2(h)(a) + h²

Example

Find: 17.1²

Nearby 17.1 is 20, and we know that 20² is 400. 'h' then is 17.1-20, which is -2.9, and (-2.9)² is 8.41, so now we can mentally solve for 17.1².

17.1² = 400 + 2(-2.9)(20) + 8.41 = 400 - 116 + 8.41 = 292.41

Proof of Method

b² = a² + 2(h)(a) + h²
b² = a² + (2)(b - a)(a) + (b - a)²
b² = a² + (2ab - 2a²) + (b² - 2ab + a²)
b² = a² + 2ab - 2a² + b² - 2ab + a²
b² = (a² - 2a² + a²) + (2ab - 2ab) + b²

b² = b²

About

I noticed this pattern in an effort to gain an edge in a "Can you guess the square root of... " game that I like to play with people in math classes. I'm sure that hundreds of people have noticed this relation before me, however I do not know who found it first. Please contact me if you know!