Answer
$x = 13.5$
To check to see if our solution is correct, we plug it into the original equation:
$\sqrt[3] {2(13.5)} = 3$
Multiply what is inside the radical sign:
$\sqrt[3] {27} = 3$
Take the cube root:
$3 = 3$
The two sides are equal; therefore, the solution is correct.
Work Step by Step
First, we need to get rid of the radical by raising each side of the equation to the third power:
$2x = 3^3$
Evaluate the right side of the equation:
$2x = 27$
Divide both sides of the equation by $2$:
$x = 13.5$
To check to see if our solution is correct, we plug it into the original equation:
$\sqrt[3] {2(13.5)} = 3$
Multiply what is inside the radical sign:
$\sqrt[3] {27} = 3$
Take the cube root:
$3 = 3$
The two sides are equal; therefore, the solution is correct.