Question

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

4396−−−√+44−−√−2275−−−√


(1 point)
Responses

3165−−−√
3 square root of 165

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

1611−−√
16 square root of 11

211−−√

Answer 1

incorrect, for you have the numbers askew!

Answer 2

To simplify the expression \(\sqrt{4396} + \sqrt{44} - \sqrt{2275}\), we first need to simplify each radical if possible.

1. **Simplifying \(\sqrt{4396}\)**:
\[
4396 = 4 \times 1099
\]
\[
\sqrt{4396} = \sqrt{4 \times 1099} = \sqrt{4} \times \sqrt{1099} = 2\sqrt{1099}
\]

2. **Simplifying \(\sqrt{44}\)**:
\[
44 = 4 \times 11
\]
\[
\sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \times \sqrt{11} = 2\sqrt{11}
\]

3. **Simplifying \(\sqrt{2275}\)**:
\[
2275 = 25 \times 91 = 25 \times (7 \times 13)
\]
\[
\sqrt{2275} = \sqrt{25 \times 91} = 5\sqrt{91}
\]

Now we can substitute back into the expression:
\[
2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91}
\]

Since \( \sqrt{1099} \), \( \sqrt{11} \), and \( \sqrt{91} \) are all unlike radicals, we cannot combine them into a single radical expression. Thus, we write the expression as:
\[
2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91}
\]

The expression is in simplest radical form and nothing can be combined further.

Thus, the answer is:
**Unlike radicals cannot be combined using addition.**

Answer 3

I apologize for any confusion in my previous response. Let's carefully recompute \(\sqrt{4396} + \sqrt{44} - \sqrt{2275}\) step by step.

### Step 1: Simplifying the radicals

1. **\(\sqrt{4396}\)**
- The prime factorization of 4396 might be helpful.
- Dividing by 4 gives \(4396 \div 4 = 1099\):
- \(\sqrt{4396} = \sqrt{4 \times 1099} = 2\sqrt{1099}\).

2. **\(\sqrt{44}\)**
- The prime factorization of 44:
- \(44 = 4 \times 11\):
- \(\sqrt{44} = \sqrt{4 \times 11} = 2\sqrt{11}\).

3. **\(\sqrt{2275}\)**
- The prime factorization of 2275:
- \(2275 = 25 \times 91 = 25 \times 7 \times 13\):
- \(\sqrt{2275} = \sqrt{25 \times 91} = 5\sqrt{91}\).

### Step 2: Substitute back into the expression

Now substituting the simplified radicals back into the expression:
\[
2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91}
\]

### Step 3: Can we combine these?

The terms \(2\sqrt{1099}\), \(2\sqrt{11}\), and \(-5\sqrt{91}\) all involve different radicals, which cannot be simplified further or combined.

### Conclusion

The final expression remains:
\[
2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91}
\]

If you are looking for a numerical approximation or more specific decompositions, please let me know! Otherwise, the correct response should be:
**Unlike radicals cannot be combined using addition.**