Cubic and cube roots

Cubic and cube roots

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.
Basic Concepts: Squares and square roots, Estimating square roots, Prime factorization, Square and square roots
Related Concepts: Conversions involve squares and cubic, Operations with radicals, Conversion between entire radicals and mixed radicals

Lessons

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
  • 1.
    Understanding the negative cube roots of the following
    a)
    327{^3}\sqrt{27}
    - 327{^3}\sqrt{27}
    3−27 {^3}\sqrt{-27}

  • 2.
    Find the cube roots
    a)
    3−4913{^3}\sqrt{-4913}

    b)
    31331 {^3}\sqrt{1331}

    c)
    −32197-{^3}\sqrt{2197}

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15.
Radicals
15.1
Square and square roots
15.2
Cubic and cube roots
15.3
Evaluating and simplifying radicals
15.4
Converting radicals to mixed radicals
15.5
Converting radicals to entire radicals
15.6
Adding and subtracting radicals
15.7
Multiplying and dividing radicals
15.8
Rationalize the denominator
Transition Year Maths
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