To simplify the expression \(\sqrt{4396} + \sqrt{44} - \sqrt{2275}\), we will first simplify each radical individually.
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Simplifying \(\sqrt{4396}\):
- Find the prime factorization of \(4396\): \(4396 = 4 \times 1099 = 2^2 \times 1099\).
- Since 1099 has no perfect square factors, we have: \[ \sqrt{4396} = \sqrt{4 \times 1099} = 2\sqrt{1099}. \]
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Simplifying \(\sqrt{44}\):
- The prime factorization of \(44\) is \(4 \times 11 = 2^2 \times 11\): \[ \sqrt{44} = \sqrt{4 \times 11} = 2\sqrt{11}. \]
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Simplifying \(\sqrt{2275}\):
- The prime factorization of \(2275\) is \(25 \times 91 = 5^2 \times 91\).
- Since 91 has no perfect square factors, we have: \[ \sqrt{2275} = \sqrt{25 \times 91} = 5\sqrt{91}. \]
Now we can rewrite the original expression in terms of these simpler radicals: \[ 2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91}. \]
Since each of these radicals involves different numbers under the square root (as all are in simplest form), we cannot combine them further. Thus, the expression remains:
\[ 2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91}. \]
None of the provided options seem to directly correspond to this expression. So, the best conclusion is that unlike radicals cannot be combined using addition, leading us to the option:
Unlike radicals cannot be combined using addition.
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