Does x^3 - 3x + 3sqrt(3) = have a constructible root? my solution: suppose a is a constructible root of the equation above. we square both sides to get x^6 - 6x^4 + 9x^2 = 27. since a is constructible, a^2 is constructible as well and we can turn this equation into cubic poly with rational coefficients, and it becomes y^3 - 6y^2 + 9y - 27 = 0. If this cubic poly has a constructible root, it must have a rational root in form of m/n. (m/n)^3 - 6(m/n)^2 + 9(m/n) = 27. How do I proceed from here? Detailed steps would be appreciated..