To find the length of AB, we can use the Pythagorean theorem.

Given that AB = 8 and tan^2(BAC) = √5 / 2, we can calculate the length of AC by taking the square root of (√5 / 2)^2.

Since tan(BAC) = AC/AB, we have tan(BAC) = AC / 8.

Solving for AC, we get AC = 8 tan(BAC) = 8 √5 / 2 = 4√5.

Now, we can use the Pythagorean theorem to find the length of AB:

AB^2 = AC^2 + BC^2
8^2 = (4√5)^2 + BC^2
64 = 80 + BC^2
BC^2 = 64 - 80
BC^2 = -16

Since BC is a length, it cannot be negative, so there seems to be an error in the given information. It is not possible to determine the exact length of AB under these conditions.