a)|5|-|-5|=5-5=0
[tex]b) |1 + \sqrt{2} | + |1 - \sqrt{2} | = 1 + \sqrt{2} + \sqrt{2} - 1 = \sqrt{2} + \sqrt{2} = 2 \sqrt{2} = 1 \sqrt{2} + 1 \sqrt{2} = (1 + 1) \sqrt{2} = 2 \sqrt{2} [/tex]
[tex]c) |2 - \sqrt{5} | \times | \sqrt{5} - 1 | = ( \sqrt{5} - 2) \times ( \sqrt{5} - 1) = \sqrt{5} \sqrt{5} - \sqrt{5} - 2 \sqrt{5} - 2 \times ( - 1) = 5 - \sqrt{5} - 2 \sqrt{5} + 2 = 7 - 3 \sqrt{5} [/tex]
[tex]d) | \sqrt{13} - 4 | + |3 - \sqrt{13} | = 4 - \sqrt{13} + 3 - \sqrt{13} = 4 - 3 = 1 [/tex]
