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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 cube root of, end cube root .
Finding the cube root of a number is the opposite of cubing a number.
Example:
start color #7854ab, 3, end color #7854ab, times, start color #7854ab, 3, end color #7854ab, times, start color #7854ab, 3, end color #7854ab = start color #7854ab, 3, end color #7854ab, start superscript, start color #ff00af, 3, end color #ff00af, end superscript, equals, start color #1fab54, 27, end color #1fab54
So root, start index, start color #ff00af, 3, end color #ff00af, end index = start color #7854ab, 3, end color #7854ab
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:
cube root of, 64, end cube root, equals, start text, question mark, end text
Here is the factor tree for 64:
So the prime factorization of 64 is 2, times, 2, times, 2, times, 2, times, 2, times, 2.
We're looking for cube root of, 64, end cube root, so we want to split the prime factors into three identical groups.
Notice that we can rearrange the factors like so:
64, equals, 2, times, 2, times, 2, times, 2, times, 2, times, 2, equals, left parenthesis, 2, times, 2, right parenthesis, times, left parenthesis, 2, times, 2, right parenthesis, times, left parenthesis, 2, times, 2, right parenthesis
So left parenthesis, 2, times, 2, right parenthesis, cubed, equals, 4, cubed, equals, 64.
So cube root of, 64, end cube root is 4.

Practice

Problem 1
cube root of, 125, end cube root, equals, start text, question mark, end text
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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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