Explicație pas cu pas:
[tex]( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3} ) = \sqrt{5} \times \sqrt{5} + \sqrt{5} \times \sqrt{3} - \sqrt{3} \times \sqrt{5} + \sqrt{3} \times \sqrt{3} = \sqrt{25} + \sqrt{15} - \sqrt{15 } + \sqrt{9} = 5 + 3 = 8[/tex]
[tex]( \sqrt{6} + 1)( \sqrt{6} - 1) = \\ \sqrt{6} \times \sqrt{6} - \sqrt{6} \times 1 + 1 \times \sqrt{6} - 1 \times 1 \\ \sqrt{36} - \sqrt{6 } + \sqrt{6} - 1 = \\ 6 - 1 = 5[/tex]
[tex](3 \sqrt{2} - 2 \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3} ) = \\ 3 \sqrt{2} \times 3 \sqrt{2} + 3 \sqrt{2} \times 2 \sqrt{3} - 2 \sqrt{3} \times 3 \sqrt{2} + 2 \sqrt{3} \times 2 \sqrt{3} \\ 9 \sqrt{4} + 6 \sqrt{6} = \\ 9 \times 2 + 6 \sqrt{6} = \\ 18 + 6 \sqrt{6} [/tex]
[tex](6 \sqrt{5} + 7 \sqrt{3} )(6 \sqrt{5} - 7 \sqrt{3} ) = \\ 6 \sqrt{5} \times 6 \sqrt{5} - 6 \sqrt{5} \times 7 \sqrt{3} + 7 \sqrt{3} \times 6 \sqrt{5} - 7 \sqrt{3} \times 7 \sqrt{3} \\ 36 \sqrt{25} - 49 \sqrt{9} = \\ 36 \times 5 - 49 \times 3 = \\ 180 - 147 = 33[/tex]
