If p varies inversely as the square of q, then we can write the relationship between p and q as \(p = \frac{k}{q^2}\), where k is a constant of proportionality. We can find the value of k using the information that p=8 when q=4: \(8 = \frac{k}{4^2}\), so \(k = 128\).

Now, we can use this value of k to find q when p=32: \(32 = \frac{128}{q^2}\), so \(q^2 = 4\). Taking the square root of both sides, we get \(q = \pm 2\).