Simplify. \( \sqrt[5]{2048}+2 \sqrt[5]{2} \)

To simplify \( \sqrt[5]{2048} + 2 \sqrt[5]{2} \), we start by breaking down the number 2048. First, we note that \( 2048 = 2^{11} \). Therefore, we can find \( \sqrt[5]{2048} \): \[ \sqrt[5]{2048} = \sqrt[5]{2^{11}} = 2^{11/5} = 2^{2.2} = 2^2 \cdot 2^{0.2} = 4 \cdot \sqrt[5]{2} \] Now, substituting this back into the original expression: \[ \sqrt[5]{2048} + 2 \sqrt[5]{2} = 4 \sqrt[5]{2} + 2 \sqrt[5]{2} \] Combining like terms, we get: \[ (4 + 2) \sqrt[5]{2} = 6 \sqrt[5]{2} \] Thus, the simplified expression is: \[ \boxed{6 \sqrt[5]{2}} \]