# Algebra Tiles Explorations of al-Khwārizmī ’s Equation Types: Modeling al-Khwārizmī’s More Complicated Problems – Example 11

Author(s):
Günhan Caglayan (New Jersey City University)

Example 11: A problem leading to the case “squares = numbers” [Rosen 1831, 55]

To find a square, four roots of which, multiplied by three roots, restore the square with a surplus of forty-four dirhems, then the solution is:  that you multiply four roots by three roots, which gives twelve squares, equal to a square and forty-four dirhems.

Remove now one square of the twelve on account of the one square connected with the forty-four dirhems. There remain eleven squares, equal to forty-four dirhems. Make the division, the result will be four, and this is the square.

Continue to Example 12.
Back to Overview of al-Khwārizmī’s More Complicated Problems.

Günhan Caglayan (New Jersey City University), "Algebra Tiles Explorations of al-Khwārizmī ’s Equation Types: Modeling al-Khwārizmī’s More Complicated Problems – Example 11," Convergence (October 2021)