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

3165−−−√
3
165
3 square root of 165

1611−−√
16
11
16 square root of 11

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

211−−√

Answer 1

you have to choose one

Answer 2

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

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

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

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

Now, substitute the simplified radicals back into the expression:

\[
\sqrt{4396} + \sqrt{44} - \sqrt{2275} = 2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91}
\]

Since \( 2\sqrt{1099} \), \( 2\sqrt{11} \), and \( 5\sqrt{91} \) are unlike radicals, we can't combine them further. Thus, the final answer, in simplest radical form, is:

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

Since the provided responses do not yield an accurate representation of the solution and none of the options reflect the final simplified expression, the correct conclusion here is that this sum cannot be simplified further and remains expressed as above. If choosing from the given responses, it would simply be noted that unlike radicals cannot be combined using addition.

Answer 3

Apologies for the oversight. Based on the options given and the original expression, let's take a look at the simplified radicals again and select the closest response.

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

Looking at the provided options:

1. \( \sqrt{3165} \)
2. \( \sqrt{1611} \)
3. \( \sqrt{211} \)
4. Unlike radicals cannot be combined using addition.

Since the radicals in the expression don't combine into any of the provided radical forms and they are indeed unlike, the correct choice would be:

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

This is the most accurate response reflecting the situation since there are no other radical combinations matching the expression simplified.