c)
| 5 - 3√3 | - | 4√3 - 7 | - 7√3 =
3√3 > 5
7 > 4√3
= 3√3 - 5 - 7 + 4√3 - 7√3
= 7√3 - 12
= 0 - 12
= - 12 rational
d)
(√1 - √3)/√3 + (√3 - √5)/√15 + (√5 - √7)/√35 + (√7 - √9)/√63 =
= (√3 - 3)/3 + (√45 - √75)/15 + (√175 - √245)/35 + (7 - 3√7)/21
= ³⁵⁾(√3 - 3)/3 + ⁷⁾(3√5 - 5√3)/15 + ³⁾(5√7 - 7√5)/35 + ⁵⁾(7 - 3√7)/21
= (35√3 - 105 + 21√5 - 35√3 + 15√7 - 21√5 + 35 - 15√7)/105
= - 70⁽³⁵/105
= - 2/3 rational
