You can search Google using your voice, but once you get to a site then you're back to typing. Oweb Voice Input is a free Chrome extension that enables you to use your voice to search on websites. With Oweb Voice Input installed anytime that you see a search box on a website you can speak your query. On some sites Oweb Voice Input can be used to complete forms too.
Applications for Education
I tried Oweb Voice Input on a Google Form and it worked perfectly for filling in short answer questions. If you're using Google Forms to collect information from students and they need an accessibility option, Oweb Voice Input is a tool worth trying.