Why do I calculate that it is K2=- root sign 3/3?

Analysis: if the inclination of L 1 is 30, the slope of L 1 is K 1 = TG30 = √ 3/3.

Since L 1⊥L2, k 1×k2=- 1, we get √3/3×k2=- 1.

Multiplied by 3: √ 3× K2 =-3

Because √3×√3=3, therefore: √3×k2=-√3×√3.

Divided by √ 3: k2 =-√ 3.

Namely: k2=-√3.

Your calculation result k2=-√3/3 is wrong. Please look for the reason carefully.