CCSS Math: 8.EE.A.2
Review cube roots, and try some practice problems.

Cube roots

The cube root of a number is the factor that we multiply by itself three times to get that number.
The symbol for cube root is 3\sqrt[3]{} .
Finding the cube root of a number is the opposite of cubing a number.
Example:
3×3×3\purpleD3\times \purpleD3\times \purpleD3 = 33=27\purpleD3^\pink3 = \greenD{27}
So 273\sqrt[\pink3]{\greenD{27}} = 3\purpleD3
Want to learn more about finding cube roots? Check out this video.

Finding cube roots

If we can't figure out what factor multiplied by itself three times will result in the given number, we can make a factor tree.
Example:
643=?\Large{\sqrt[3]{64} = \text{?}}
Here is the factor tree for 6464:
So the prime factorization of 6464 is 2×2×2×2×2×22\times 2\times 2\times 2\times 2\times 2.
We're looking for 643\sqrt[3]{64}, so we want to split the prime factors into three identical groups.
Notice that we can rearrange the factors like so:
64=2×2×2×2×2×2=(2×2)×(2×2)×(2×2)64 = 2\times 2\times 2\times 2\times 2\times 2 = \left(2\times 2\right)\times\left(2\times 2\right)\times\left(2\times 2\right)
So (2×2)3=43=64\left(2\times 2\right)^3 = 4^3 = 64.
So 643\sqrt[3]{64} is 44.

Practice

Problem 1
1253=?\Large{\sqrt[3]{125} = \text{?}}
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Want to try more problems like this? Check out this exercise: Finding cube roots
Or this challenge exercise: Equations with square and cube roots