Using your knowledge of simplifying square roots and cube roots, complete each problem. Following the instructions, answer all of the questions, and make sure to show all of your work.

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For question 1, answer in complete sentences using math vocabulary.

1. How does simplifying a square root expression differ from simplifying a cube root expression?

For problems 2 and 3, select each true statement. Show work to justify your answers.

2. 2√56
   
   1. √56 lies between 3 and 4
   
   
   2. √56 lies between 7 and 8
   
   
   3. √56 simplifies to 2√14
   
   
   4. √56 simplifies to 2√7
      
      


3. ∛320
   
   1. ∛320 simplifies to 4∛5
   
   
   2. ∛320 simplifies to 8 ∛5
   
   
   3. ∛320 lies between 6 and 7
   
   
   4. ∛320 lies between 17 and 8

For problems 4 - 10, simplify each radical expression. Show work to justify your answers.

4. √75a⁵


5. √36c³d


6. √60xc⁷y⁴


7. √500


8. √98


9. ∛24


10. ∛-500

Once you have completed this assignment, please submit your work to the dropbox.