To combine the given radicals \( \sqrt{4396} + \sqrt{44} - \sqrt{2275} \), we need to simplify each radical first.
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Simplifying \( \sqrt{4396} \):
- \( 4396 = 4 \times 1099 \)
- \( \sqrt{4396} = \sqrt{4 \times 1099} = \sqrt{4} \times \sqrt{1099} = 2\sqrt{1099} \)
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Simplifying \( \sqrt{44} \):
- \( 44 = 4 \times 11 \)
- \( \sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \times \sqrt{11} = 2\sqrt{11} \)
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Simplifying \( \sqrt{2275} \):
- Factor \( 2275 \): \( 2275 = 25 \times 91 \)
- Since \( 25 = 5^2 \) and \( 91 = 7 \times 13 \):
- \( \sqrt{2275} = \sqrt{25 \times 91} = \sqrt{25} \times \sqrt{91} = 5\sqrt{91} \)
Now substitute the simplified radicals back into the original expression:
\[ \sqrt{4396} + \sqrt{44} - \sqrt{2275} = 2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91} \]
Since \( \sqrt{1099} \), \( \sqrt{11} \), and \( \sqrt{91} \) are unlike radicals, we cannot combine these terms further. Therefore, the final answer in simplest radical form is:
\[ 2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91} \]
None of the response options provided exactly match this expression. Only the statement "Unlike radicals cannot be combined using addition." correctly addresses the inability to combine them into one term. Thus:
Unlike radicals cannot be combined using addition.
1 answer