[tex] A + B = [/tex]
[tex] = \sqrt{27} + 5 + 4\sqrt{12} - 2 [/tex]
[tex] = 3 \sqrt{3} + 5 + 8 \sqrt {3} - 2 [/tex]
[tex] = 11 \sqrt{3} + 3 [/tex]
A + B is irrational.
[tex] A \times B = [/tex]
[tex] = (\sqrt{27} + 5)(4\sqrt{12} - 2) [/tex]
[tex] = (3 \sqrt{3} + 5)(8 \sqrt{3} - 2) [/tex]
[tex] = 24 \times 3 - 6 \sqrt{3} + 40 \sqrt{3} - 10 [/tex]
[tex] = 72 + 34 \sqrt {3} - 10 [/tex]
[tex] = 62 + 34 \sqrt{3} [/tex]
A * B is irrational.
I did one addition and one product.
Use the same method to do the other additions and products.
