SOLUTION: I homeschool my 9th grader and we have one more question on simplifying radicals. He is supposed to simplify index 3 of square root 160. My teacher's manual says the answer is:

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Question 310971: I homeschool my 9th grader and we have one more question on simplifying radicals. He is supposed to simplify index 3 of square root 160. My teacher's manual says the answer is: 2 (index 3) of square root 20. My son and I feel that 20 could be simplified. Is the teacher's manual wrong or are we. thank you. Joan and her son Jed
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I think you're getting confused on the symbols.
It's not the square root, it's the cube root.
I think that's what you mean by index 3 square root.
Just like square root is to the (1%2F2) power, cube root is to the (1%2F3) power.
You can pull the 8 out because 2%5E3=8 so the cube root of 8 is 2.
You have no other factors in 20 that are cube roots so it's as simplified as it can be.