√8р-√2р+√18о

To simplify the expression \( \sqrt{8p} - \sqrt{2p} + \sqrt{18o} \), you can start by simplifying each square root individually.

1. Simplify \( \sqrt{8p} \): \[ \sqrt{8p} = \sqrt{4 \cdot 2 \cdot p} = \sqrt{4} \cdot \sqrt{2} \cdot \sqrt{p} = 2\sqrt{2p} \]

2. Simplify \( \sqrt{2p} \):

   • This term is already simplified and remains \( \sqrt{2p} \).

3. Simplify \( \sqrt{18o} \): \[ \sqrt{18o} = \sqrt{9 \cdot 2 \cdot o} = \sqrt{9} \cdot \sqrt{2} \cdot \sqrt{o} = 3\sqrt{2o} \]

Now we can rewrite the original expression using these simplifications: \[ 2\sqrt{2p} - \sqrt{2p} + 3\sqrt{2o} \]

Next, combine like terms \( 2\sqrt{2p} - \sqrt{2p} \): \[ (2 - 1)\sqrt{2p} + 3\sqrt{2o} = \sqrt{2p} + 3\sqrt{2o} \]

Therefore, the simplified form of the expression is: \[ \sqrt{2p} + 3\sqrt{2o} \]