I am endeavoring to streamline the following mathematical expression:
expr = 200 * x**5 * y**6
sym.simplify(sym.sqrt(200 * x**5 * y**6))
However, the simplification process has not yielded the anticipated outcome. In pursuit of a resolution, I extended my investigations to encompass the simplification of sqrt(y**6) utilizing both the simplify and powsimp functions. Regrettably, neither of these approaches yielded the desired results.
Upon reflection, it has become apparent that the reluctance of SymPy to simplify sqrt(y**6) may stem from the divergence in outcomes when substituting negative values. I also undertook assessments involving sqrt(y**8) using both the simplify and powsimp functions, which, once again, proved ineffective.
Could you kindly elucidate the methodology to effectively simplify this expression? Additionally, I am intrigued by the factors contributing to SymPy’s reluctance to apply simplification. Should you possess any recommendations for supplementary resources to facilitate further exploration, I would be immensely appreciative.
>Solution :
sympy will make a sqrt divide the power by 2 if you tell it to assume the variables are positive, which is the only case where sqrt(x**6) = x**3, it is only true when x is positive.
import sympy as sym
x, y = sym.symbols('x y', positive = True)
expr = 200 * x**5 * y**6
sym.simplify(sym.sqrt(200 * x**5 * y**6))
10*sqrt(2)*x**(5/2)*y**3