Question

Combine the radicals using addition and subtraction. Give the answer in simplest radical form.

4396−−−√+44−−√−2275−−−√
4
396
+
44
−
2
275


(1 point)
Responses

Unlike radicals cannot be combined using addition.
Unlike radicals cannot be combined using addition.

1611−−√
16
11
16 square root of 11

3165−−−√
3
165
3 square root of 165

211−−√
2
11
2 square root of 11
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Answer 1

To combine the radicals in the expression \( \sqrt{4396} + \sqrt{44} - \sqrt{2275} \), we first simplify each radical.

1. **Simplify \( \sqrt{4396} \)**:
- Find the prime factorization of \( 4396 \).
- \( 4396 = 4 \times 1099 = 2^2 \times 1099 \).
- Thus, \( \sqrt{4396} = \sqrt{4 \times 1099} = \sqrt{4} \times \sqrt{1099} = 2\sqrt{1099} \).

2. **Simplify \( \sqrt{44} \)**:
- \( 44 = 4 \times 11 \).
- Thus, \( \sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \times \sqrt{11} = 2\sqrt{11} \).

3. **Simplify \( \sqrt{2275} \)**:
- Find the prime factorization of \( 2275 \).
- \( 2275 = 25 \times 91 = 5^2 \times 7 \times 13 \).
- Thus, \( \sqrt{2275} = \sqrt{25 \times 91} = \sqrt{25} \times \sqrt{91} = 5\sqrt{91} \).

Now substituting the simplified forms back into the original expression:

\[
2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91}
\]

Since \( \sqrt{1099} \), \( \sqrt{11} \), and \( \sqrt{91} \) are unlike radicals, they cannot be combined further.

Therefore, the expression in simplest radical form is:

\[
\boxed{2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91}}
\]