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 root, start index, 3, end index, square root of, end square root .
Finding the cube root of a number is the opposite of cubing a number.
Example:
start color purpleD, 3, end color purpleD, times, start color purpleD, 3, end color purpleD, times, start color purpleD, 3, end color purpleD = start color purpleD, 3, end color purpleD, start superscript, start color pink, 3, end color pink, end superscript, equals, start color greenD, 27, end color greenD
So root, start index, start color pink, 3, end color pink, end index, square root of, start color greenD, 27, end color greenD, end square root = start color purpleD, 3, end color purpleD
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:
root, start index, 3, end index, square root of, 64, end square root, equals, question mark
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 root, start index, 3, end index, square root of, 64, end square 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, start superscript, 3, end superscript, equals, 4, start superscript, 3, end superscript, equals, 64.
So root, start index, 3, end index, square root of, 64, end square root is 4.

Practice

Problem 1
root, start index, 3, end index, square root of, 125, end square root, equals, question mark
  • 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, p, i or 2, slash, 3, space, p, i

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