**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.