A non-magnetic ceramic has a relative permittivity of 36 at 500 MHz…

Step 1. The index. $n = \sqrt{\varepsilon_r\mu_r} = \sqrt{36} = 6.0$.

Step 2. The speed. $v = \dfrac{c}{n} = \dfrac{3.00 \times 10^{8}\ \text{m/s}}{6.0} = 5.00 \times 10^{7}\ \text{m/s}$.

Step 3. The wavelength. $\lambda = \dfrac{v}{f} = \dfrac{5.00 \times 10^{7}\ \text{m/s}}{500 \times 10^{6}\ \text{Hz}} = 0.100\ \text{m}$.