Finding Rational Solutions for ψ in √(87600-1.44ψ^2) with ψ ≤ 10

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SUMMARY

The discussion focuses on finding rational solutions for ψ in the equation √(87600-1.44ψ^2) with the constraint that ψ must be less than or equal to 10. Participants suggest substituting specific values for ψ, such as ψ=5, to compute the square root and identify nearby rational numbers. The equation can be rearranged to solve for ψ by setting √(87600-1.44ψ^2) equal to a rational number r. The primary goal is to determine the permissible values of ψ under the given conditions.

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

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