To simplify the expression \( \sqrt{50} - 2\sqrt{8} \), we start by simplifying each radical term.
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Simplify \( \sqrt{50} \): \[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \]
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Simplify \( 2\sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \] Therefore, \[ 2\sqrt{8} = 2 \cdot 2\sqrt{2} = 4\sqrt{2} \]
Now, substitute these simplified forms back into the original expression: \[ \sqrt{50} - 2\sqrt{8} = 5\sqrt{2} - 4\sqrt{2} \]
Now combine like terms: \[ 5\sqrt{2} - 4\sqrt{2} = (5 - 4)\sqrt{2} = 1\sqrt{2} = \sqrt{2} \]
Thus, the simplified expression is: \[ \sqrt{2} \]