Finding rational values of √(87600-1.44ψ²) for ψ ≤ 10

[luckis11]

How can I find the values for ψ that the following sqaure root equals to a rational number?:
√(87600-1.44ψ^2)

Also, I don't want ψ to be greater than 10. What's the procedure to find the answer?

 

[mathman]

Does ψ have any restrictions except size? If not, try any value of ψ which is allowable (say ψ=5), compute the square root. Find a rational number near this square root and compute ψ for this rational number.

 

[TylerH]

Let: √(87600-1.44ψ^2) = r, where r is a rational number
solve for ψ
set restrictions on values of ψ