The answer to your question depends on whether the root name in question is trademarked. While only a lawyer can give you legal advice, what you seem to want to do will probably get you into trouble. Most business do claim either a registered or unregistered trademark on their domain names.
Here's a nice example from Ebay of your problem:
A trademark is a name or logo used by a company to identify its goods or services. For example, eBay® is the name of our company, but it is also a trademark used on our site and on various eBay products. Coca Cola® is a trademark used in the sale of soft drinks. Many trademarks are registered, but a trademark need not be registered for an owner to protect it. Trademark laws are primarily designed to protect consumers from confusing one company's goods or services with those of another.
Trademark infringement usually involves using someone's trademark on a good or service in a way that may confuse others about the source or affiliation of the goods or services. For example, if a seller unauthorized by or unaffiliated with Nike® sells sports clothes called "Nikestuff," the seller is probably infringing Nike’s trademark. There are other ways to infringe a trademark, including registering domain names that are substantially similar to the name of a trademark owner.
If a person operates a website using a domain name that contains someone else's trademark (for example, "www.nikestuff.com"), people who see or visit that domain name are likely to be confused and believe that the site is affiliated with Nike when it is not. People may also mistakenly go to this website thinking it's connected with the other company, only to find out that it is not. Intentional misspellings of and similarities to trademarked names (for example, www.wwwebay.com, www.amizon.com) may also be considered trademark infringements. Just because a company hasn't registered all variations of its name or trademark as domain names doesn't mean that others can use those domain names. If the domain names are likely to confuse consumers, they're probably infringing.
In 1999, the United States Congress passed the Anticybersquatting Consumer Protection Act, which generally prohibits using a domain name containing another's trademark with an intent to profit. That law allows penalties of up to $100,000 per domain name abuse incident; anyone who in bad faith uses, sells, or tries to sell a domain name that infringes another's trademark may be fined.