√160с+2√40с-3√90с

To simplify the expression \( \sqrt{160c} + 2\sqrt{40c} - 3\sqrt{90c} \), we will simplify each square root term first. 1. **Simplify \( \sqrt{160c} \)**: \[ \sqrt{160c} = \sqrt{16 \cdot 10 \cdot c} = \sqrt{16} \cdot \sqrt{10} \cdot \sqrt{c} = 4\sqrt{10c} \] 2. **Simplify \( 2\sqrt{40c} \)**: \[ 2\sqrt{40c} = 2\sqrt{4 \cdot 10 \cdot c} = 2 \cdot \sqrt{4} \cdot \sqrt{10} \cdot \sqrt{c} = 2 \cdot 2\sqrt{10c} = 4\sqrt{10c} \] 3. **Simplify \( -3\sqrt{90c} \)**: \[ -3\sqrt{90c} = -3\sqrt{9 \cdot 10 \cdot c} = -3 \cdot \sqrt{9} \cdot \sqrt{10} \cdot \sqrt{c} = -3 \cdot 3\sqrt{10c} = -9\sqrt{10c} \] Now, substitute these simplified terms back into the expression: \[ 4\sqrt{10c} + 4\sqrt{10c} - 9\sqrt{10c} \] Combine the like terms: \[ (4 + 4 - 9)\sqrt{10c} = -1\sqrt{10c} = -\sqrt{10c} \] Thus, the simplified expression is: \[ -\sqrt{10c} \]