Answer
$x = 23$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {23 + 2} = 5$
Evaluate what is inside the radical:
$\sqrt {25} = 5$
Evaluate the square root:
$5 = 5$
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 square both sides of the equation:
$x + 2 = 5^{2}$
Evaluate the right side of the equation:
$x + 2 = 25$
Subtract $2$ from both sides of the equation to solve for $x$:
$x = 23$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {23 + 2} = 5$
Evaluate what is inside the radical:
$\sqrt {25} = 5$
Evaluate the square root:
$5 = 5$
The two sides of the equation are equal; therefore, our solution is correct.