To combine the radicals \(\sqrt{396} + \sqrt{44} - 2\sqrt{275}\), we first simplify each radical.
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Simplifying \(\sqrt{396}\): \[ 396 = 4 \times 99 = 4 \times 9 \times 11 = 36 \times 11 \] Therefore, \[ \sqrt{396} = \sqrt{36 \times 11} = \sqrt{36} \times \sqrt{11} = 6\sqrt{11} \]
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Simplifying \(\sqrt{44}\): \[ 44 = 4 \times 11 \] Therefore, \[ \sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \times \sqrt{11} = 2\sqrt{11} \]
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Simplifying \(\sqrt{275}\): \[ 275 = 25 \times 11 \] Therefore, \[ \sqrt{275} = \sqrt{25 \times 11} = \sqrt{25} \times \sqrt{11} = 5\sqrt{11} \] So, \[ 2\sqrt{275} = 2 \times 5\sqrt{11} = 10\sqrt{11} \]
Now we can substitute the simplified radicals back into the expression: \[ \sqrt{396} + \sqrt{44} - 2\sqrt{275} = 6\sqrt{11} + 2\sqrt{11} - 10\sqrt{11} \]
Next, we combine like terms: \[ (6 + 2 - 10)\sqrt{11} = -2\sqrt{11} \]
Thus, the answer in simplest radical form is: \[ \boxed{-2\sqrt{11}} \]
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