Write \( \sqrt{11}+\sqrt{99} \) in the form \( a \sqrt{b} \) where \( a \) and \( b \) are integers.

To write \( \sqrt{11} + \sqrt{99} \) in the form \( a \sqrt{b} \), we start by simplifying \( \sqrt{99} \). We know that: \[ \sqrt{99} = \sqrt{9 \times 11} = \sqrt{9} \cdot \sqrt{11} = 3\sqrt{11} \] Now we can rewrite the original expression: \[ \sqrt{11} + \sqrt{99} = \sqrt{11} + 3\sqrt{11} \] Combining like terms, we get: \[ \sqrt{11} + 3\sqrt{11} = (1 + 3)\sqrt{11} = 4\sqrt{11} \] Thus, the expression \( \sqrt{11} + \sqrt{99} \) in the form \( a\sqrt{b} \) is: \[ \boxed{4\sqrt{11}} \]