Question

30/02
Show that 12 cos 30° + 2 tan 60° can be written in the form √k where k is an integer. ​

Answer 1

√192

Explanation:

Recall from a 30-60-90 triangle:

sin 30° = 1/2 sin 60° = √3/2

cos 30° = √3/2 cos 60° = 1/2

tan 30° = √3/2 tan 60° = √3

12 cos 30° + 2 tan 60° =

= 12 × √3/2 + 2 × √3

= 6√3 + 2√3

= 8√3

= √64 × √3

= √192