# Algebra Tiles Explorations of al-Khwārizmī ’s Equation Types: Modeling al-Khwārizmī’s More Complicated Problems – Example 12

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

Example 12: A problem leading to the case “squares = numbers” [Rosen 1831, 55]

A square, four of the roots of which multiplied by five of its roots produce twice the square, with a surplus of thirty-six dirhems; then the solution is: that you multiply four roots by five roots, which gives twenty squares, equal to two squares and thirty-six dirhems.

Remove two squares from the twenty on account of the other two. The remainder is eighteen squares, equal to thirty-six dirhems. Divide now thirty-six dirhems by eighteen; the quotient is two, and this is the square.

Continue to Example 13.
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 12," Convergence (October 2021)