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[tex]\dfrac{ \sqrt{27} + \sqrt{75} }{\sqrt{48}} = \dfrac{ \sqrt{9 \times 3} + \sqrt{25 \times 3}}{\sqrt{16 \times 3}} = \dfrac{3 \sqrt{3} + 5 \sqrt{3}}{4 \sqrt{3}} = \dfrac{8 \sqrt{3}}{4 \sqrt{3}} = 2[/tex]