Add 28–√ + 28−−√ + 28–√

.(1 point)
Responses

58–√
5 Start Root 8 End Root

48–√ + 28−−√
4 Start Root 8 End Root plus Start Root 28 End Root

544−−√
5 Start Root 44 End Root

416−−√ + 28−−√

1 answer

To add \( \sqrt{28} + \sqrt{28} + \sqrt{28} \), we first recognize that this simplifies to:

\[ 3 \sqrt{28} \]

Next, we should simplify \( \sqrt{28} \). We can factor \( 28 \) as follows:

\[ \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2 \sqrt{7} \]

Therefore, we have:

\[ 3 \sqrt{28} = 3 \times 2 \sqrt{7} = 6 \sqrt{7} \]

Now, let's check the provided options for match:

  1. \( \sqrt{58} \)
  2. \( 5 \sqrt{8} \)
  3. \( 4 \sqrt{8} + \sqrt{28} \)
  4. \( 5 \sqrt{44} \)
  5. \( 4 \sqrt{16} + \sqrt{28} \)

None of these options equal \( 6 \sqrt{7} \), but if we analyze option 3:

\[ 4 \sqrt{8} + \sqrt{28} = 4 (2 \sqrt{2}) + 2 \sqrt{7} = 8 \sqrt{2} + 2 \sqrt{7} \]

This also does not match.

Therefore, it seems that none of these options directly corresponds to \( 6 \sqrt{7} \). The correct conclusion is that \( \sqrt{28} + \sqrt{28} + \sqrt{28} = 6 \sqrt{7} \), but none of the options provided matches this result.