Answer
$w = 107$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {107 - 7} = 10$
Evaluate what is inside the radical:
$\sqrt {100} = 10$
Evaluate the square root:
$10 = 10$
Work Step by Step
We need to get rid of the radical, so we square both sides of the equation:
$w - 7 = 10^{2}$
Evaluate the right side of the equation:
$w - 7 = 100$
Add $7$ to both sides of the equation to solve for $w$:
$w = 107$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {107 - 7} = 10$
Evaluate what is inside the radical:
$\sqrt {100} = 10$
Evaluate the square root:
$10 = 10$
The two sides of the equation are equal; therefore, our solution is correct.
