Step 1 :Given the expression \(-7 \sqrt{3}-2 \sqrt{3}+7 \sqrt{6}\), we need to simplify it by combining the radical terms using the indicated operation(s).
Step 2 :Identify the like terms in the expression. In this case, the like terms are \(-7 \sqrt{3}\) and \(-2 \sqrt{3}\).
Step 3 :Add the coefficients of the like terms. The coefficients of the like terms are -7 and -2. Adding these gives -9.
Step 4 :The term \(7 \sqrt{6}\) cannot be combined with the other terms because it is not a like term.
Step 5 :Combine the results from the previous steps to form the simplified expression. The simplified expression is \(-9 \sqrt{3} + 7 \sqrt{6}\).
Step 6 :Final Answer: The simplified expression is \(\boxed{-9 \sqrt{3} + 7 \sqrt{6}}\).