Initial program 35.8
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
Initial simplification35.7
\[\leadsto \sqrt[3]{\frac{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}{a \cdot 2}} + \sqrt[3]{\frac{\frac{-1}{2}}{a} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}\]
- Using strategy
rm Applied associate-*l/35.8
\[\leadsto \sqrt[3]{\frac{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}{a \cdot 2}} + \sqrt[3]{\color{blue}{\frac{\frac{-1}{2} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}{a}}}\]
Applied cbrt-div33.7
\[\leadsto \sqrt[3]{\frac{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}{a \cdot 2}} + \color{blue}{\frac{\sqrt[3]{\frac{-1}{2} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}}{\sqrt[3]{a}}}\]
- Using strategy
rm Applied cbrt-div32.1
\[\leadsto \color{blue}{\frac{\sqrt[3]{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}}{\sqrt[3]{a \cdot 2}}} + \frac{\sqrt[3]{\frac{-1}{2} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}}{\sqrt[3]{a}}\]
- Using strategy
rm Applied add-sqr-sqrt32.7
\[\leadsto \frac{\sqrt[3]{\color{blue}{\sqrt{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g} \cdot \sqrt{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}}}}{\sqrt[3]{a \cdot 2}} + \frac{\sqrt[3]{\frac{-1}{2} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}}{\sqrt[3]{a}}\]
Final simplification32.7
\[\leadsto \frac{\sqrt[3]{\sqrt{\sqrt{\left(h + g\right) \cdot \left(g - h\right)} - g} \cdot \sqrt{\sqrt{\left(h + g\right) \cdot \left(g - h\right)} - g}}}{\sqrt[3]{a \cdot 2}} + \frac{\sqrt[3]{\frac{-1}{2} \cdot \left(\sqrt{\left(h + g\right) \cdot \left(g - h\right)} + g\right)}}{\sqrt[3]{a}}\]
