(i) (11 + \(\sqrt11\))(11 - \(\sqrt11\)) = (11)2 - (\(\sqrt11\))2
Because (a + b)(a - b) = a2 - b2
= 121 - 11 = 110
(ii) (5 + \(\sqrt7\))(5 - \(\sqrt7\)) = (5)2 - (\(\sqrt7\))2
= 25 – 7 = 18
(iii) (\(\sqrt8\) - \(\sqrt2\))(\(\sqrt8\) + \(\sqrt2\)) = (\(\sqrt8\))2 - (\(\sqrt2\))2
= 8 – 2 = 6
(iv) (3 + \(\sqrt3\))(3 - \(\sqrt3\)) = (3)2 - (\(\sqrt3\))2
= 9 – 3 = 6
(v) (\(\sqrt5\) - \(\sqrt2\))(\(\sqrt5\) - \(\sqrt2\)) = (\(\sqrt5\))2 - (\(\sqrt2\))2
= 5 – 2 = 3