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Cube roots review

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 A3 .
Finding the cube root of a number is the opposite of cubing a number.
3×3×3 = 33=27
So A273 = 3
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.
Here is the factor tree for 64:
A factor tree of 64. The number 64 is the product of 2 and 32. The 2 is circled. The 32 is a product of 2 and 16. The 2 is circled. The 16 is a product of 2 and 8. The 2 is circled. The 8 is a product of 2 and 4. The 2 is circled. The 4 is a product of 2 and 2. Both 2's are circled.
So the prime factorization of 64 is 2×2×2×2×2×2.
We're looking for A643, so we want to split the prime factors into three identical groups.
Notice that we can rearrange the factors like so:
So (2×2)3=43=64.
So A643 is 4.


Problem 1
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 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

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