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\((\sqrt{15}+\sqrt {3})^2\)
\(=15+3+2\sqrt{45}\)
\(=18+2\sqrt{45}\)

আবার, \((\sqrt{12}+\sqrt{6})^2\)
\(=12+6+2\sqrt{72}\)
\(=18+2\sqrt{72}\)

যেহেতু, \(\sqrt{72}\gt \sqrt{45}\)
\(\therefore 18+2\sqrt{72} \gt 18+2\sqrt{45}\)
বা, \((\sqrt{12}+\sqrt{6})^2 \gt (\sqrt{15}+\sqrt {3})^2\)
বা, \((\sqrt{12}+\sqrt{6}) \gt (\sqrt{15}+\sqrt {3})\)

\(\therefore \sqrt{12}+\sqrt{6}\) বৃহত্তর ।