As parents, we like our children to think we are invincible and the smartest person in the world. However, if our purpose is to raise children that can function in society and get great careers, that may not be the best thing to do.
Telling our children that we were wrong shows them that we do not know everything, and that apologizing when wrong about something is both good and healthy.
The best way to apologize is to simply say that you are sorry, no long explanation is needed. This act will help a child grow and become an emotionally mature adult. Letting children know that you do not know everything, and helping them to research answers, will help them in school as well as the job market later in life.