Question

Express in surd form and simplify by rationalizing the denominator. 
3 sin⁡ 45° - 2 cos⁡ 30°
         tan⁡ 30°

Answer 1

sin 45º = ¹/_√2 × ^√2/_√2 = ^√2/_√2
Cos 30º = ^√3/₂
Tan 30º = ¹/_√3 × ^√3/_√3 = ^√3/₃
(3 ^√2/₂ - 2 ^√3/₂ )/^√3/₃
3 √2 - 2√3
 2^√3/₃
(9√2 - 6√3) √3
   2√3 (√3)
=9√6 - 18
       6
^{3√6 - 6}/₂
or ^3√6/₂ - 3