The formula z = sqrt (x^2 + y^2) is an equation for solving for one side of a right triangle if the other two sides are known. It is derived from the Pythagorean theorem, z^2 = x^2 + y^2, by taking the square root of both sides of the equation.
The Pythagorean theorem states that for any right triangle, the sum of the squares of the two legs equals the square of the hypotenuse. For example, if the legs of a right triangle are 3 and 4 feet long respectively, the length of the hypotenuse is found by adding 3^2 and 4^2 and taking the square root of that sum. It can also be worked in reverse. For example, if hypotenuse z and leg x are known, the length of leg y can be found by taking the square root of (z^2 - x^2).