Find All Complex Solutions x^3=16

$x^{3} = 16$

Step 1

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{16}$

Step 2

Simplify $\sqrt[3]{16}$ .

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$x = \sqrt[3]{8 (2)}$

Rewrite $8$ as $2^{3}$ .

$x = \sqrt[3]{2^{3} \cdot 2}$

Pull terms out from under the radical.

$x = 2 \sqrt[3]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt[3]{2}$

Decimal Form:

$x = 2.51984209 \dots$