Prove that 12 cos(30°) - 2 tan(60°) can be written as √k where k is an integer, state the value of k.

Conversion of trigonometric functions:

cos(30°) = √3 / 2

tan(60°) = √3

Computing equation with trigonometric substitutions:

12 cos(30°) - 2 tan(60°) = 12 (√3 / 2) - 2 (√3) = (12 / 2) x √3 - 2√3 = 6√3 - 2√3 = 4√3

Rearranging into requested form:

4√3 = √4² x √3 = √16 x √3 = √48

Stating k:

√k = √48

k = 48