tan(a + b) = (tan a + tan b) / (1 - tan a tan b)
Let's apply this formula to find the value of tan 195:
tan 195 = tan (180 + 15) = (tan 180 + tan 15) / (1 - tan 180 tan 15) = (-tan 15) / (1 - 0) = -tan 15
Now, we need to express tan 15 in simple surd form. We can use the half-angle formula for tangent:
tan (a/2) = sin a / (1 + cos a)
Let's apply this formula to find tan 15:
tan 15 = tan (30/2) = sin 30 / (1 + cos 30) = (1/2) / (1 + √3/2) = (1/2) / (2 + √3) = (1/2) * (2 - √3) = √3/6
Therefore, tan 195 in simple surd form is -√3/6.