If you do not want the iPad to store history of what websites you browse in its storage, you can make use of private or incognito mode on most mobile web browsers. This is available on Safari, Chrome, Firefox for iPad. Keep in mind that going incognito will not hide your IP or stop websites from tracking you.
In Safari > tap on the tab bar icon > Private. In Chrome for iPad, tap on the three dots > new incognito tab and in Firefox > tap on the mask icon to start private browsing.
Also, if you do not want your searches to be stored, you can use duckduckgo.com as this website promises that it would not collect any personal information from the searches you do on the iPad or any other device.