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

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In summary, the purpose of finding rational solutions for ψ in √(87600-1.44ψ^2) with ψ ≤ 10 is to solve for the values of ψ that will make the expression equal to a rational number, which is important in various mathematical and scientific applications. This can be achieved by simplifying the expression and setting it equal to a rational number, and the restriction of ψ ≤ 10 makes the solutions more manageable. There can be multiple rational solutions for ψ, and some real-life applications of this process include engineering and scientific fields.
  • #1
luckis11
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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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  • #2
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.
 
  • #3
Let: √(87600-1.44ψ^2) = r, where r is a rational number
solve for ψ
set restrictions on values of ψ
 

1. What is the purpose of finding rational solutions for ψ in √(87600-1.44ψ^2) with ψ ≤ 10?

The purpose of finding rational solutions for ψ in √(87600-1.44ψ^2) with ψ ≤ 10 is to solve for the values of ψ that will make the expression equal to a rational number. This can help in further mathematical calculations and analyses.

2. How do you find rational solutions for ψ in √(87600-1.44ψ^2) with ψ ≤ 10?

To find rational solutions for ψ in √(87600-1.44ψ^2) with ψ ≤ 10, we need to first simplify the expression by factoring out the square root and then setting it equal to a rational number. This can be done by using various algebraic techniques such as completing the square or using the quadratic formula.

3. Why is it important for ψ to be less than or equal to 10 in this expression?

The restriction of ψ ≤ 10 is important because it limits the range of possible solutions and makes the expression easier to work with. Without this restriction, the solutions could be infinitely large and more difficult to analyze.

4. Can there be more than one rational solution for ψ in √(87600-1.44ψ^2) with ψ ≤ 10?

Yes, there can be multiple rational solutions for ψ in √(87600-1.44ψ^2) with ψ ≤ 10. This is because the expression contains a square root, which can have both positive and negative solutions. Additionally, since we are dealing with rational numbers, there can be multiple fractions that can satisfy the equation.

5. What are some real-life applications of finding rational solutions for ψ in √(87600-1.44ψ^2) with ψ ≤ 10?

One real-life application of finding rational solutions for ψ in √(87600-1.44ψ^2) with ψ ≤ 10 is in the field of engineering, where it can be used to solve for specific values in mathematical models and equations. It can also be applied in various scientific fields, such as physics and chemistry, to find rational solutions for physical quantities and variables.

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