How do i claim my dependent's college room and board?

The cost of room and board is not an allowable tax deduction, accept as it pertains to reducing the taxable amount of earnings on a college savings plan. If you withdraw money form a tax advantaged college savings plan, you need to spend the distribution from the plan on education expenses or the earnings will be taxable. You can include room and board for education expenses for that, but otherwise they are not deductible or available for an education credit. You would enter your room and board, if needed, when you enter your Form 1098-T in the Deductions and Credits section of TurboTax, then Education, then Expenses and Scholarships (Form 1098-T).

Room and board (R&B)are not a qualified expense for a tuition credit or for tax free scholarship.  As such, there is not where to enter R&B, in TurboTax (TT). 

There is an exception. R&B is a qualified expenses for a 529 plan (or ESA) distribution. TT will give you an entry point for R&B, but you must have previously entered your 1099-Q for the 529 distribution. 

To get the screen to enter Room & Board, answer yes when asked if you have book expenses, in the 1098-T section.