Add and Subtract Radicals Quick Check

Question

3 of 53 of 5 Items
Question
Add 22−−√3 + 322−−√ + 22−−√
.(1 point)
Responses

522−−√
5 Start Root 22 End Root

566−−√
5 Start Root 66 End Root

22−−√3 + 422−−√
root index 3 Start Root 22 End Root plus 4 Start Root 22 End Root

22−−√3 + 444−−√

Answer 1

To simplify the expression \( \sqrt{22} - \sqrt{3} + 3\sqrt{22} + \sqrt{22} \), we can combine like terms.

1. Identify the terms involving \( \sqrt{22} \):

   • \( \sqrt{22} + 3\sqrt{22} + \sqrt{22} = 5\sqrt{22} \)

2. The term involving \( \sqrt{3} \) remains as is:

   • \( -\sqrt{3} \)

Now, combining these gives us:

\[ 5\sqrt{22} - \sqrt{3} \]

Thus, among the answer choices provided, the simplified expression is:

Correct response: \( 5\sqrt{22} - \sqrt{3} \) (translated from the context, could not find an exact option among the above choices).

Please verify if there's a missing option that presents this form. If summarizing as options, remember \( \sqrt{22} \) and \( \sqrt{3} \) cannot be combined, thus forms are maintained separately.