What is the sixth root of 64?

Answer 1

2

64 is also 26, so the sixth root of 26 is 2.

In general, the n-th root of Xn is X.

ALTERNATIVE ANSWER:

The Fundamental Theorem of Algebra states that every polynomial of degree n has n (possibly complex) roots.

This means that there are 6 sixth roots of 64.

These roots are:

2*w, 2*w^2, 2*w^3, 2*w^4, 2 * w^5 and 2 * w^6

where w is the 6th root of unity, or

w = e^(2πi/6) = cos(2π / 6) + i * sin (2π / 6)

Note that w^3 = -1 and w^6 = 1, so there are actually two real sixth roots: 2 and -2. The other four are imaginary/complex.