Why do radicals react quickly to form covalent bonds with nearby substances?

To be stable and achieve octet rule free radicals quickly make covalent bonds with the nearby substances.

Explanation:

Every atoms tend to have eight electrons in its outermost shell, this is octet rule. The number of electron is equal to number of protons in the atom. The atom either shares, takes or gives up electrons order to achieve octet rule.

For example, Sodium (Na) with atomic number 11 with only one electron in outermost shell and the shell below it has 8 electrons. To satisfy the rule it has to give up one electron by making covalent bond with any other atom that accepts this electron.