Answer
$x = 59$
To check if our solution is correct, we plug it into the original equation:
$\sqrt [3] {59 + 5} = 4$
Evaluate what is inside the radical:
$\sqrt [3] {64} = 4$
Evaluate the square root:
$4 = 4$
The two sides of the equation are equal; therefore, our solution is correct.
Work Step by Step
We need to get rid of the radical, so we cube both sides of the equation:
$x + 5 = 4^{3}$
Evaluate the right side of the equation:
$x + 5 = 64$
Subtract $5$ from both sides of the equation to solve for $x$:
$x = 59$
To check if our solution is correct, we plug it into the original equation:
$\sqrt [3] {59 + 5} = 4$
Evaluate what is inside the radical:
$\sqrt [3] {64} = 4$
Evaluate the square root:
$4 = 4$
The two sides of the equation are equal; therefore, our solution is correct.
