1)
[tex] ( \sqrt{3} + \sqrt{2} ) \times \sqrt{2} = \sqrt{3} \times \sqrt{2} + \sqrt{2} \times \sqrt{2} [/tex]
[tex] = \sqrt{6} + \sqrt{4} = \sqrt{6} + 2[/tex]
2)
[tex]( \sqrt{3} - \sqrt{4} )(1 + \sqrt{2} ) = [/tex]
[tex] = \sqrt{3} \times 1 + \sqrt{3 } \times \sqrt{2} - \sqrt{4} \times 1 - \sqrt{4} \times \sqrt{2} [/tex]
[tex] = \sqrt{3} + \sqrt{6} - \sqrt{4} - \sqrt{8} = [/tex]
[tex] = \sqrt{3} + \sqrt{6} - 2 - 2 \sqrt{2} [/tex]
4)
[tex]( \sqrt{8} + \sqrt{2} )(1 + \sqrt{2} ) = [/tex]
[tex] = \sqrt{8} \times 1 + \sqrt{2} \times 1 + \sqrt{8} \times \sqrt{2} + \sqrt{2} \times \sqrt{2} [/tex]
[tex] = \sqrt{8} + \sqrt{16} + \sqrt{2} + \sqrt{4} = [/tex]
[tex] = 2 \sqrt{2} + 4 + \sqrt{2} + 2 = [/tex]
[tex] = 3 \sqrt{2} + 6 = 3( \sqrt{2} + 3) [/tex]
3)
[tex](3 + \sqrt{2} )(1 + \sqrt{2} ) = [/tex]
[tex] = 3 \times 1 + \sqrt{2} \times 1 + 3 \times \sqrt{2 } + \sqrt{2} \times \sqrt{2} = [/tex]
[tex] = 3 + \sqrt{2} + 3 \sqrt{2} + \sqrt{4} = [/tex]
[tex] = 3 + 4 \sqrt{2} + 2 = [/tex]
[tex] = 5 + 4 \sqrt{2} [/tex]
5)
[tex]( - \sqrt{3} + \sqrt{2} )(1 + \sqrt{2} ) = [/tex]
[tex] = - \sqrt{3} \times 1 + \sqrt{2} \times 1 - \sqrt{3} \times \sqrt{2} + \sqrt{2} \times \sqrt{2} [/tex]
[tex] = - \sqrt{3} + \sqrt{2} - \sqrt{6} + \sqrt{4} [/tex]
[tex] = - \sqrt{3} + \sqrt{2} - \sqrt{6} + 2[/tex]
