Cube roots review

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 $\sqrt[3]{}$cube root of, end cube root .

Finding the cube root of a number is the opposite of cubing a number.

$\purpleD3\times \purpleD3\times \purpleD3$start color #7854ab, 3, end color #7854ab, times, start color #7854ab, 3, end color #7854ab, times, start color #7854ab, 3, end color #7854ab = $\purpleD3^\pink3 = \greenD{27}$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 $\sqrt[\pink3]{\greenD{27}}$root, start index, start color #ff00af, 3, end color #ff00af, end index = $\purpleD3$start color #7854ab, 3, end color #7854ab

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$64:

So the prime factorization of $64$64 is $2\times 2\times 2\times 2\times 2\times 2$2, times, 2, times, 2, times, 2, times, 2, times, 2.

We're looking for $\sqrt[3]{64}$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:

So $\left(2\times 2\right)^3 = 4^3 = 64$left parenthesis, 2, times, 2, right parenthesis, cubed, equals, 4, cubed, equals, 64.

So $\sqrt[3]{64}$cube root of, 64, end cube root is $4$4.

Want to try more problems like this? Check out this exercise: Finding cube roots

Or this challenge exercise: Equations with square and cube roots