To find the total length of the three pieces of wood when expressed in simplest radical form, we first simplify each radical:
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Simplifying \( \sqrt{200} \): \[ \sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \cdot \sqrt{2} = 10\sqrt{2} \]
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Simplifying \( \sqrt{72} \): \[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2} \]
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Simplifying \( \sqrt{18} \): \[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} \]
Next, we find the total length by adding these simplified radicals together: \[ 10\sqrt{2} + 6\sqrt{2} + 3\sqrt{2} \]
Combining these: \[ (10 + 6 + 3)\sqrt{2} = 19\sqrt{2} \]
Thus, the total length of the wood is: \[ \boxed{19\sqrt{2}} \]