Solve h^2=500^2+1000

$$h ^ { 2 } = 500 ^ { 2 } + 1000$$

Solve for h

$$h=10\sqrt{2510}\approx 500.999001995$$

$$h=-10\sqrt{2510}\approx -500.999001995$$

Steps by Finding Square Root

Calculate 500 to the power of 2 and get 250000.

$$h^{2}=250000+1000$$

Add 250000 and 1000 to get 251000.

$$h^{2}=251000$$

Take the square root of both sides of the equation.

$$h=10\sqrt{2510} h=-10\sqrt{2510}$$

Steps Using the Quadratic Formula

Calculate 500 to the power of 2 and get 250000.

$$h^{2}=250000+1000$$

Add 250000 and 1000 to get 251000.

$$h^{2}=251000$$

Subtract 251000 from both sides.

$$h^{2}-251000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -251000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{0±\sqrt{0^{2}-4\left(-251000\right)}}{2}$$

Square 0.

$$h=\frac{0±\sqrt{-4\left(-251000\right)}}{2}$$

Multiply -4 times -251000.

$$h=\frac{0±\sqrt{1004000}}{2}$$

Take the square root of 1004000.

$$h=\frac{0±20\sqrt{2510}}{2}$$

Now solve the equation h=\frac{0±20\sqrt{2510}}{2} when ± is plus.

$$h=10\sqrt{2510}$$

Now solve the equation h=\frac{0±20\sqrt{2510}}{2} when ± is minus.

$$h=-10\sqrt{2510}$$

The equation is now solved.

$$h=10\sqrt{2510} h=-10\sqrt{2510}$$