The formula for looking for the volume of a square pyramid is [tex]s^2 \frac{h}{3} [/tex].
s²h/3 = 200
s²h = 600
s²(s-4) = 600
s³ - 4s² - 600 = 0
(s - 10)(s² + 6s + 60) = 0
The second factor s² + 6s + 60 would have factors (s + _ ) (s + _ ) where the blanks are not necessarily equal but are positive. This would mean that s would have a negative value so we do not take that.
The only possible length of the square base is 10 inches. The height being 6 inches.
