$$y^4 = 400$$
Answer
$$ \begin{matrix}y_1 = 4.47214 & y_2 = -4.47214 & y_3 = 4.47214i \\[1 em] y_4 = -4.47214i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} y^4 &= 400&& \text{move all terms to the left hand side } \\[1 em]y^4-400 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Polynomial Equations Solver