When we're asked to find the
cube of a number, we're asked repeatedly multiply that number by itself 3 times. For instance, if we wanted to find the cube of 2 (2³), we'd find

which, in this case, equals 8. On the other hand, when we're asked to take the
cube root of a number, we're being asked to find out which number, when multiplied by itself 3 times, gives us the number under the root sign. In our last example, finding the cube root of 8 (∛8) gets us:
![\sqrt[3]{8} =2](https://img.qammunity.org/2018/formulas/mathematics/middle-school/cd18ysmxvlsof1ix6fyxj3ot6nkilopdjx.png)
since 2 x 2 x 2 = 8.
In your problem, we're being asked: "What number multiplied by itself gives us 64?" Or: ? x ? x ? = 64. Finding that answer takes some knowledge of the factors of 64. 64's prime factorization is

, or 2 x 2 x 2 x 2 x 2 x 2. If we pair up all of the twos, we can rewrite this product as

or

since 4, when multiplied by itself 3 times, gives us 64, we know it must be our answer.