## 3 Results and Discussion
### Comparison of the Utilized Extraction Methods in This Study  
Different extraction methods (MAC, SOX, MAE, UAE, UMAE, and MUAE) were used in this study to extract quercetin and total flavonoids from red onion skin. Optimum extraction conditions include microwave time of 60 s, ultrasound time of 15 min, ultrasound temperature of 70 \({}^{\circ}\)C, ethanol concentration of 70% (\(\tau/v\), water), solvent-to-solid ratio of 30 mL/g, microwave power of 180W, ultrasound power of 100%, ultrasound frequency of 37 kHz and particle size of 180 \(\upmu\)m were applied for quercetin recovery. In addition, extraction conditions at microwave time of 60 s, ultrasound time of 15 min, ultrasound temperature of 60 \({}^{\circ}\)C, ethanol concentration of 60% (\(\tau/v\), water), solvent-to-solid ratio of 30 mL/g, microwave power of 180 W, ultrasound power of 100%, ultrasound frequency of 37 kHz and particle size of 180 \(\upmu\)m were investigated for total flavonoid extraction. The results (Table 5) showed that the highest extraction yield was obtained from the MUAE process, followed by UMAE, UAE, MAE, SOX, and MAC. The classification of different flavonoid content in the extract samples is presented in Table 6. Also, the HPLC analysis result of the extracted sample is shown in Figure 5. The analysis highlights the variety and concentration of key compounds, such as quercetin and its derivatives, in the extracted samples. For instance, quercetin (C\({}_{15}\)H\({}_{10}\)O\({}_{7}\)) had the highest concentration at 5.43 \(\pm\) 0.06% with a retention time of 13.60 min, indicating its significant presence in the extract. Other notable compounds, such as quercetin 4\({}^{\prime}\)-O-glucoside (C\({}_{21}\)H\({}_{20}\)O\({}_{12}\)), were found at 3.15 \(\pm\) 1.20% with a retention time of 10.50 min. While certain compounds like isorhamnetin 3_A_\({}^{\prime}\)-diglucoside (C\({}_{28}\)H\({}_{32}\)O\({}_{17}\)) and kaempfer (C\({}_{15}\)H\({}_{10}\)O\({}_{6}\)) were identified, some, including isorhamnetin derivatives, were not detected (ND), which could be attributed to their instability or low concentrations in the extraction process. This detailed flavonoid profile provides insights into the effectiveness of the extraction method and highlights the significant recovery of quercetin and its derivatives in the samples.  
Figure 4: The correlation between numerical and experimental data.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Extraction Method** & **QE (\%)** & **TFC (\%)** \\ \hline MAC & 2.96 \(\pm\) 0.03 \({}^{\mathrm{f}}\) & 3.64 \(\pm\) 0.02 \({}^{\mathrm{f}}\) \\ SOX & 3.09 \(\pm\) 0.05 \({}^{\mathrm{e}}\) & 5.24 \(\pm\) 0.03 \({}^{\mathrm{e}}\) \\ MAE & 5.03 \(\pm\) 0.02 \({}^{\mathrm{d}}\) & 7.91 \(\pm\) 0.06 \({}^{\mathrm{d}}\) \\ UAE & 5.36 \(\pm\) 0.0 \({}^{\mathrm{c}}\) & 8.34 \(\pm\) 0.05 \({}^{\mathrm{c}}\) \\ UMAE & 7.66 \(\pm\) 0.04 \({}^{\mathrm{b}}\) & 10.18 \(\pm\) 0.14 \({}^{\mathrm{b}}\) \\ MUAE & 10.32 \(\pm\) 0.18 \({}^{\mathrm{a}}\) & 12.52 \(\pm\) 0.20 \({}^{\mathrm{a}}\) \\ \hline \hline \end{tabular} \% = mg QE/g DOS \(\times\) 100; MAC: maceration; SOX: Soxhlet extraction; MAE: microwave-assisted extraction; UAE: ultrasound-assisted extraction; MUAE: microwave-assisted extraction; MUAE: microwave/ultrasound-assisted extraction; TFC: total flavonoid content; QE: quercetin equivalents; data are expressed as means \(\pm\) SD (n = 3); mean values with different letters are significantly different (\(p<\) 0.05).  
\end{table}
Table 5: Comparison of recovery yields from different extraction methods.