Systematic Treatise on Mathematics, Volume 6

Diagram of the Square, Side-Strips, and Corner Method

The "corner method" (yufa) refers to a primary square with two "side-strips" attached, leaving a small square at the corner, which is the "corner" (yu). This visualizes the formula $(a+b)^2 = a^2 + 2ab + b^2$, where $a^2$ is the square, $2ab$ are the side-strips, and $b^2$ is the corner.

The side of the square is 18 steps.

Extracting the Square Root Extracting the Square Root (kaipingfang): The process of finding the side length of a square when only its area is known.
Where there is a dividend The total area or number to be rooted. but no divisor, one must estimate the quotient to divide it.

The "side-strip method" (lianfa) refers to a primary square with two rectangular strips attached to its sides to bolster its form; these are the "side-strips" (lian).

The area of the square is 324 square steps.

The method says: Set the area of 324 steps as the dividend (shi).
○ Estimate the first quotient of 10 at the left of the dividend.
Below the method, also place 10 to the right of the dividend.
This is called the "square method" (fangfa); it corresponds to the quotient above. Essentially $a \times a$, or $10 \times 10$.
1 times 1 [10 x 10] removes 100 from the dividend, leaving a remainder of 224.
Then, double the "square method" value of 10 to get 20; this is called the "side-strip method" (lianfa). This represents the $2ab$ part of the binomial expansion, preparing to find $b$. ○
Again, estimate the second quotient of 8 steps at the left. Adding this to the first quotient of 10 makes a total of 18 steps. Also place 8 steps at the dividend... The text continues the calculation, showing how 18 is derived as the root.