√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:

\[ -\sqrt{10c} \]