[tex] \sqrt{75 \:} - \: \sqrt{12 \: } + \sqrt{108} [/tex]

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[tex] \sqrt{75} - \sqrt{12} + \sqrt{108} [/tex]

[tex] = \sqrt{25 \times 3} - \sqrt{4 \times 3} + \sqrt{36 \times 3} [/tex]

[tex] = 5 \sqrt{3} - 2 \sqrt{3} + 6 \sqrt{3} [/tex]

[tex] = 9 \sqrt{3} [/tex]

[tex] \sqrt{75} - \sqrt{12} + \sqrt{108} \\ = \sqrt{5 \times 5 \times 3} - \sqrt{2 \times 2 \times 3} + \sqrt{6 \times 6 \times 3} \\ = 5 \sqrt{3} - 2 \sqrt{3} + 6 \sqrt{3} \\ = 9 \sqrt{3} [/tex]