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Add 22−−√3 + 322−−√ + 22−−√.(1 point)%0D%0AResponses%0D%0A%0D%0A22−−√3 + 444−−√%0D%0Aroot index 3 Start Root 22 End Root plus 4 Start Root 44 End Root%0D%0A%0D%0A522−−√%0D%0A5 Start Root 22 End Root%0D%0A%0D%0A22−−√3 + 422−−√%0D%0Aroot index 3 Start Root 22 End Root plus 4 Start Root 22 End Root%0D%0A%0D%0A566−−√

3 answers

To simplify the expression \( \sqrt{22} \cdot 3 + 32 \sqrt{22} \), let's break it down step by step.

  1. Rewrite the given expression: \[ \sqrt{22} \cdot 3 + 32 \sqrt{22} \]

  2. Combine like terms: Since both terms contain \( \sqrt{22} \), we can factor it out: \[ \sqrt{22}(3 + 32) \]

  3. Calculate the values inside the parentheses: \[ 3 + 32 = 35 \]

  4. Therefore, the expression simplifies to: \[ \sqrt{22} \cdot 35 = 35\sqrt{22} \]

Hence, the proper way to write the final answer is: \[ 35 \sqrt{22} \]

This matches none of the options given at the start, so it seems there might have been a misunderstanding in the expression to be simplified. Based on the closest options, if correcting our approach to \( \sqrt{22} \cdot 3 + 4\sqrt{44} \):

  • The second term, \(4 \sqrt{44}\), simplifies as follows: \[ \sqrt{44} = \sqrt{4 \cdot 11} = 2\sqrt{11} \] So \(4\sqrt{44} = 8\sqrt{11}\).

In this case, you'd end up with: \[ \sqrt{22} \cdot 3 + 8\sqrt{11} \] As this does not seem to match your options, please check or clarify the original terms provided.

1. 10sqrt21
2. 2sqrt19
3. ^3sqrt22 + 4sqrt22
4. 7sqrt23
5. 2sqrt6

Based on your original question and the new options you've provided, it appears there may have been some confusion regarding the initial expression.

To clarify, let's break down the computation of \( \sqrt{22} \cdot 3 + 32 \sqrt{22} \) again and see if it aligns more closely with one of the options you provided:

  1. Start with the expression \( 3\sqrt{22} + 32\sqrt{22} \).
  2. Combine the like terms: \[ (3 + 32)\sqrt{22} = 35\sqrt{22} \]

Since 35 is not in any of the options:

  • Let's now directly evaluate the new options you provided.

  1. \(10\sqrt{21}\): This does not relate to our numbers.

  2. \(2\sqrt{19}\): This also does not relate.

  3. \(\sqrt{22} + 4\sqrt{22}\): This can be simplified: \[ \sqrt{22} + 4\sqrt{22} = (1 + 4)\sqrt{22} = 5\sqrt{22} \] This value was also not the answer we derived.

  4. \(7\sqrt{23}\): This doesn’t relate to our work.

  5. \(2\sqrt{6}\): This is different again.

Given the computations and options presented, the computed value \(35\sqrt{22}\) does not correspond to any of your listed options.

It seems there may have been a miscommunication on what expression to simplify. If you clarify the original problem, I can assist further in identifying how to align them to these options or revise as necessary. Based on your computation steps, it appears none of the options are equivalent to \(35\sqrt{22}\). Please confirm the expression for the simplification, or investigate whether any option is equivalent to another form.