Simplify: \( 5 \sqrt{54}+2 \sqrt{175}-1 \sqrt{24}-5 \sqrt{7} \) (entry tip: to type type "5sqrt(3x)" - no quotes) \( \square> \) Next Question

Let's simplify the expression step by step: \[ 5\sqrt{54} + 2\sqrt{175} - \sqrt{24} - 5\sqrt{7} \] 1. **Simplify each square root:** - \(\sqrt{54} = \sqrt{9 \times 6} = 3\sqrt{6}\) - \(\sqrt{175} = \sqrt{25 \times 7} = 5\sqrt{7}\) - \(\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}\) 2. **Substitute back into the expression:** \[ 5 \times 3\sqrt{6} + 2 \times 5\sqrt{7} - 2\sqrt{6} - 5\sqrt{7} \] 3. **Multiply the coefficients:** \[ 15\sqrt{6} + 10\sqrt{7} - 2\sqrt{6} - 5\sqrt{7} \] 4. **Combine like terms:** - Combine the \(\sqrt{6}\) terms: \(15\sqrt{6} - 2\sqrt{6} = 13\sqrt{6}\) - Combine the \(\sqrt{7}\) terms: \(10\sqrt{7} - 5\sqrt{7} = 5\sqrt{7}\) 5. **Final simplified expression:** \[ 13\sqrt{6} + 5\sqrt{7} \] **Answer:** \[ 13 \sqrt{6} + 5 \sqrt{7} \]