[tex]\sqrt{27} + \sqrt{147} = \sqrt{48} + \sqrt{n}\\ \sqrt{27} = 3 \sqrt{3}\\ \sqrt{147} = 7 \sqrt{3}\\ \sqrt{48} = 4 \sqrt{3}\\ \sqrt{27} + \sqrt{147} - \sqrt{48}= \sqrt{n}\\ 3 \sqrt{3} + 7 \sqrt{3} - 4 \sqrt{3} = \sqrt{n}\\ 6 \sqrt{3} = \sqrt{n} => \\ \sqrt{n} = \sqrt{108} = > n =108[/tex]