How do I destroy Nekker nests?

In "The Nekker Contract" quest, I need to destroy all of the Nekker nests. I found my first Nekker nest, but when I try to destroy it, Geralt just says, "I've got to blow up this nest," and doesn't do anything.

So I assume that I need something to blow it up—what would that be?

Screenshot of a Nekker nest with the left-click "destroy nest" option:

Solution 1:

You find out the way to destroy the Nekker nests by obtaining enough knowledge about the Nekkers, either by reading a book about them (available in Flotsam) or by fighting them. If you're at knowledge level 3/3 (character screen -> Attributes -> Knowledge) there will be the following text about the Nekkers

Witchers can user their full range of skills and techniques when fighting nekkers. Signs, bombs, poisons and oils that augment bleeding are all extremely effective against the beasts. Nekker nests are best destroyed with Grapeshot bombs.

To build a Grapeshot bomb you first need the schematic, which is available from the elf Cedric. Just look out for the craftsman icon on the map in Lebinden to find him. After you bought the schematic you need to meditate and then build some Grapeshot bombs:

Thanks to Justin for the hint on how to destroy the nests.

Solution 2:

You need a bomb called Grapeshot. You can get the recipe from Cedric in Lebinden.