Initial program 34.9
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
Applied simplify34.9
\[\leadsto \color{blue}{\sqrt[3]{\frac{\left(-g\right) + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{a + a}} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{a + a}}}\]
- Using strategy
rm Applied add-cube-cbrt34.9
\[\leadsto \sqrt[3]{\frac{\left(-g\right) + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{\color{blue}{\left(\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}\right) \cdot \sqrt[3]{a + a}}}} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{a + a}}\]
Applied *-un-lft-identity34.9
\[\leadsto \sqrt[3]{\frac{\color{blue}{1 \cdot \left(\left(-g\right) + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}}{\left(\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}\right) \cdot \sqrt[3]{a + a}}} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{a + a}}\]
Applied times-frac34.9
\[\leadsto \sqrt[3]{\color{blue}{\frac{1}{\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}} \cdot \frac{\left(-g\right) + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{\sqrt[3]{a + a}}}} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{a + a}}\]
Applied cbrt-prod33.0
\[\leadsto \color{blue}{\sqrt[3]{\frac{1}{\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}}} \cdot \sqrt[3]{\frac{\left(-g\right) + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{\sqrt[3]{a + a}}}} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{a + a}}\]
- Using strategy
rm Applied add-cube-cbrt33.1
\[\leadsto \sqrt[3]{\frac{1}{\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}}} \cdot \sqrt[3]{\frac{\left(-g\right) + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{\sqrt[3]{a + a}}} + \sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{\color{blue}{\left(\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}\right) \cdot \sqrt[3]{a + a}}}}\]
Applied add-cube-cbrt33.1
\[\leadsto \sqrt[3]{\frac{1}{\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}}} \cdot \sqrt[3]{\frac{\left(-g\right) + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{\sqrt[3]{a + a}}} + \sqrt[3]{\frac{\color{blue}{\left(\sqrt[3]{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}\right) \cdot \sqrt[3]{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}}}{\left(\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}\right) \cdot \sqrt[3]{a + a}}}\]
Applied times-frac33.1
\[\leadsto \sqrt[3]{\frac{1}{\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}}} \cdot \sqrt[3]{\frac{\left(-g\right) + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{\sqrt[3]{a + a}}} + \sqrt[3]{\color{blue}{\frac{\sqrt[3]{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}}{\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}} \cdot \frac{\sqrt[3]{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}}{\sqrt[3]{a + a}}}}\]
Applied cbrt-prod31.2
\[\leadsto \sqrt[3]{\frac{1}{\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}}} \cdot \sqrt[3]{\frac{\left(-g\right) + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}{\sqrt[3]{a + a}}} + \color{blue}{\sqrt[3]{\frac{\sqrt[3]{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}}{\sqrt[3]{a + a} \cdot \sqrt[3]{a + a}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\left(-g\right) - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}}{\sqrt[3]{a + a}}}}\]
- Removed slow
pow expressions.
