Combine like terms in the following expression: \( 3\sqrt{2} - 5\sqrt{8} + \sqrt{32} \)

To combine like terms, we first simplify each term that involves a square root. 1. The term \(-5\sqrt{8}\): Since \(\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}\), we have: \[ -5\sqrt{8} = -5 \times 2\sqrt{2} = -10\sqrt{2} \] 2. The term \(\sqrt{32}\): Similarly, since \(\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}\), we find: \[ \sqrt{32} = 4\sqrt{2} \] Now, we can rewrite the entire expression using these simplifications: \[ 3\sqrt{2} - 10\sqrt{2} + 4\sqrt{2} \] Next, we combine the coefficients of \(\sqrt{2}\): \[ (3 - 10 + 4)\sqrt{2} = -3\sqrt{2} \] So, the final answer after combining like terms is: \[ -3\sqrt{2} \]