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

Question

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

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 2

incorrect, for you have the numbers askew!

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.