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

4396−−−√+44−−√−2275−−−√


(1 point)
Responses

211−−√
2 square root of 11

3165−−−√
3 square root of 165

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

1611−−√

1 answer

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

  1. Simplifying \( \sqrt{4396} \):

    • We can factor 4396: \[ 4396 = 4 \times 1099 \]
    • Thus, \[ \sqrt{4396} = \sqrt{4 \times 1099} = \sqrt{4} \times \sqrt{1099} = 2\sqrt{1099} \]
  2. Simplifying \( \sqrt{44} \):

    • We can factor 44: \[ 44 = 4 \times 11 \]
    • Thus, \[ \sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \times \sqrt{11} = 2\sqrt{11} \]
  3. Simplifying \( \sqrt{2275} \):

    • We can factor 2275: \[ 2275 = 25 \times 91 = 25 \times (7 \times 13) \]
    • Thus, \[ \sqrt{2275} = \sqrt{25 \times 91} = \sqrt{25} \times \sqrt{91} = 5\sqrt{91} \]

Now we substitute these simplified forms back into the original expression: \[ \sqrt{4396} + \sqrt{44} - \sqrt{2275} = 2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91} \]

Since none of the radicals are like terms, we cannot combine them further.

Therefore, the final answer in simplest radical form is: \[ 2\sqrt{1099} + 2\sqrt{11} - 5\sqrt{91} \] However, this form does not appear to correspond directly to any of the response options you provided. If you need further help matching to those options, please let me know!