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
[tex]2\times2\times2[/tex]
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:
[tex] \sqrt[3]{8} =2[/tex]
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 [tex]2^6[/tex], 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
[tex](2\times2)\times(2\times2)\times(2\times2)[/tex]
or
[tex]4\times4\times4=4^3[/tex]
since 4, when multiplied by itself 3 times, gives us 64, we know it must be our answer.
