a)
(6 - √3)/√27 - (√3 + 2)/√12 - (1 + √3)/√3 =
= (6 - √3)/3√3 - (√3 + 2)/2√3 - (1 + √3)/√3
= √3(6 - √3)/9 - √3(√3 + 2)/6 - √3(1 + √3)/3
= 3(2√3 - 1)/9 - (3 + 2√3)/6 - (√3 + 3)/3
= [2(2√3 - 1) - 3 - 2√3 - 2(√3 + 3)]/6
= (4√3 - 2 - 3 - 2√3 - 2√3 - 6)/6
= - 11/6 rational
b)
(√2 - 10)/5√2 - (2 - √2)/2√2 + (9 - 2√2)3√2 =
= √2(√2 - 10)/10 - √2(2 - √2)/4 + √2(9 - 2√2)/6
= 2(1 - 5√2)/10 - (2√2 - 2)/4 + (9√2 - 4)/6
= ⁶⁾(1 - 5√2)/5 - ¹⁵⁾(√2 - 1)/2 + ⁵⁾(9√2 - 4)/6
= (6 - 30√2 - 15√2 + 15 + 45√2 - 20)/30
= 1/30 rational
