To radiate is to give off energy. So for example, an oven radiates heat energy. To irradiate is to give something radioactive properties. For example, exposure to nuclear radiation will irradiate something.

To "radiate" is "to send out in every direction." Usually it means light or energy, but not necessarily. The spokes of a wheel radiate from the hub. To "irradiate" is "to bathe in radiation." The sun radiates light. The grass is irradiated by sunlight. In the scientific field of radiometry, the unit of "radiance" is "watts per steradian per square metre," and the unit of "irradiance" is "watts per square metre."

irradiate sth with sth faces irradiated with joy radiate from sb/sth Her voice hadn't changed but I felt the anger that radiated from her.