3)
[tex]a = \sqrt{55 - 12 \sqrt{21}} \\ = \sqrt{27 + 28 - 12 \sqrt{3} \times \sqrt{7} } \\ = \sqrt{27 - 2 \times 3 \sqrt{3} \times 2 \sqrt{7} + 28 } \\ = \sqrt{(3 \sqrt{3}) ^{2} - 2 \times 3 \sqrt{3} \times 2 \sqrt{7} + (2 \sqrt{7}) ^{2} } \\ = \sqrt{(3 \sqrt{3} - 2 \sqrt{7} ) ^{2} } \\ = 3 \sqrt{3 } - 2 \sqrt{7} [/tex]
