Answer
$x = 11$
To check if our solution is correct, substitute it back into the original equation:
$\sqrt {5 + 11} = 4$
Simplify the radical:
$\sqrt {16} = 4$
Evaluate the square root:
$4 = 4$
The two sides are equal; therefore, the solution is correct.
Work Step by Step
Square both sides of the equation:
$5 + x = 4^{2}$
Evaluate the right side of the equation:
$5 + x = 16$
Subtract $5$ from each side of the equation to solve for $x$:
$x = 11$
To check if our solution is correct, substitute it back into the original equation:
$\sqrt {5 + 11} = 4$
Simplify the radical:
$\sqrt {16} = 4$
Evaluate the square root:
$4 = 4$
The two sides are equal; therefore, the solution is correct.
