My son is in 4th grade and needs to simplify the cube roots of 216, 512 and 64. How does he do this with a regular calculator or without?
I would certainly discourage the use of a calculator to solve this problem. I would use "intelligent guess and check".
The first thing to notice is that 2x2x2 = 8, so 2 is too small to be the cube root of any of the three numbers. On the other hand 10x10x10 = 1000 so 10 is too large to be the cube root af any of the three numbers.
Next try something in between, say 5. Multiplying 5x5x5 = 25x5 = 125 shows that the cube root of 64 is less than 5 and the cube roots of 216 and 512 are larger than 5.
Lets focus on 64 first. I know now its cube root is larger than 2 and smaller than 5 so try 3 or 4.
Once you are done with 64 continue looking for the cube roots of 216 and 512. You know that both cube roots are larger than 5 and smaller than 10 so try one of 6, 7, 8 and 9.
Intelligent guess and check is a really valuable technique.Cheers,