Add 22−−√3 + 322−−√ + 22−−√

Question

.(1 point)
Responses

522−−√
5 Start Root 22 End Root

566−−√
5 Start Root 66 End Root

22−−√3 + 444−−√
root index 3 Start Root 22 End Root plus 4 Start Root 44 End Root

22−−√3 + 422−−√

Answer 1

To add \( 2\sqrt{3} + 3\sqrt{2} + 2\sqrt{2} \), we first need to combine the like terms:

1. The terms \( 3\sqrt{2} \) and \( 2\sqrt{2} \) can be combined: \[ 3\sqrt{2} + 2\sqrt{2} = (3 + 2)\sqrt{2} = 5\sqrt{2} \]

2. Now, including the other term: \[ 5\sqrt{2} + 2\sqrt{3} \]

Thus, the final result is:

\[ 2\sqrt{3} + 5\sqrt{2} \]

None of the options perfectly reflect this sum. However, it seems like you are looking for an expression similar to \( 5\sqrt{2} + 2\sqrt{3} \).

If the answer choice contains \( 5\sqrt{2} \) and \( 2\sqrt{3} \) (or simply \( 2\sqrt{3} + 5\sqrt{2} \) under a different order), then that would be the correct response.