Add and Subtract Radicals Quick Check

Question

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

522−−√
5 Start Root 22 End Root

566−−√
5 Start Root 66 End Root

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

^3 22−−√3 + 444−−√

Answer 1

To add the radicals \( \sqrt{22} + \sqrt{22} + \sqrt{22} \), we can treat each term as a like term.

So:

\[ \sqrt{22} + \sqrt{22} + \sqrt{22} = 3\sqrt{22} \]

Based on the options provided, none of them exactly match the \( 3\sqrt{22} \) we calculated, but here's a breakdown of the options you posted:

1. \( 5\sqrt{22} \)
2. \( 5\sqrt{66} \)
3. \( \sqrt[3]{22} + 4\sqrt{22} \)
4. \( \sqrt[3]{22} + 4\sqrt{4} \)

If these choices are representing an addition of three \( \sqrt{22} \) terms, option 3 would be the closest choice for understanding what to do with \( \sqrt{22} \) but doesn't represent the total correctly.

Thus, the answer to the question is simply:

\[ 3\sqrt{22} \]

If choosing an answer is required based on your listed options and depending on what it means (if it asks to recalculate or similar), option 3 might be a misrepresentation contextually or simply needs clarification.