√8р-√2р+√18р

To simplify the expression \( \sqrt{8p} - \sqrt{2p} + \sqrt{18p} \), we can break down each term under the square root. 1. Simplifying \( \sqrt{8p} \): \[ \sqrt{8p} = \sqrt{4 \cdot 2 \cdot p} = \sqrt{4} \cdot \sqrt{2} \cdot \sqrt{p} = 2\sqrt{2p} \] 2. Simplifying \( \sqrt{2p} \): \[ \sqrt{2p} = \sqrt{2} \cdot \sqrt{p} \] (This term stays as is since it's already in its simplest form.) 3. Simplifying \( \sqrt{18p} \): \[ \sqrt{18p} = \sqrt{9 \cdot 2 \cdot p} = \sqrt{9} \cdot \sqrt{2} \cdot \sqrt{p} = 3\sqrt{2p} \] Now, substituting these simplified terms back into the expression gives: \[ 2\sqrt{2p} - \sqrt{2p} + 3\sqrt{2p} \] Next, we can combine the like terms: \[ (2 - 1 + 3)\sqrt{2p} = 4\sqrt{2p} \] Thus, the simplified expression is: \[ \boxed{4\sqrt{2p}} \]