Cubic and cube roots

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  1. Understanding the negative cube roots of the following
    1. 327{^3}\sqrt{27}
      - 327{^3}\sqrt{27}
      327 {^3}\sqrt{-27}
  2. Find the cube roots
    1. 34913{^3}\sqrt{-4913}
    2. 31331 {^3}\sqrt{1331}
    3. 32197-{^3}\sqrt{2197}
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Topic Notes
Whenever we see "roots", let it be cubic roots or square roots, we know for sure that we will need to do prime factorization to find out the prime factors of the numbers. In this section, we use factors and multiples to find perfect cube whole numbers and cubic roots.
To cube:
Raise the number to the third power
Ex: 33 {3^3} =3×3×3=27= 3\times 3\times 3 = 27
63 {6^3} = 6×6×6=2166\times 6\times 6 = 216

To cube root:
Finding the three identical factors
Ex: 364 {^3}\sqrt{64} = 34×4×4{^3}\sqrt{4\times 4\times 4} = 4
3125 {^3}\sqrt{125} = 35×5×5{^3}\sqrt{5\times 5\times 5} = 5

Perfect Cubes:
03 {0^3}= 0
13 {1^3} = 1
23 {2^3} = 8
33 {3^3} = 27
43 {4^3} = 64
53 {5^3} = 125
63 {6^3} = 216
73 {7^3} = 343
83 {8^3} = 512
93 {9^3} = 729
103 {10^3} = 1000