Question
$$1.029 = 3r^3$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 1.029 &= 3r^3&& \text{move all terms to the left hand side } \\[1 em]1-3r^3 &= 0&& \text{simplify left side} \\[1 em]-3r^3+1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver