Solve h^2=37^2+25^2

$$h ^ { 2 } = 37 ^ { 2 } + 25 ^ { 2 }$$

Solve for h

$$h=\sqrt{1994}\approx 44.654227124$$

$$h=-\sqrt{1994}\approx -44.654227124$$

Steps by Finding Square Root

Calculate 37 to the power of 2 and get 1369.

$$h^{2}=1369+25^{2}$$

Calculate 25 to the power of 2 and get 625.

$$h^{2}=1369+625$$

Add 1369 and 625 to get 1994.

$$h^{2}=1994$$

Take the square root of both sides of the equation.

$$h=\sqrt{1994} h=-\sqrt{1994}$$

Steps Using the Quadratic Formula

Calculate 37 to the power of 2 and get 1369.

$$h^{2}=1369+25^{2}$$

Calculate 25 to the power of 2 and get 625.

$$h^{2}=1369+625$$

Add 1369 and 625 to get 1994.

$$h^{2}=1994$$

Subtract 1994 from both sides.

$$h^{2}-1994=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1994 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{0±\sqrt{0^{2}-4\left(-1994\right)}}{2}$$

Square 0.

$$h=\frac{0±\sqrt{-4\left(-1994\right)}}{2}$$

Multiply -4 times -1994.

$$h=\frac{0±\sqrt{7976}}{2}$$

Take the square root of 7976.

$$h=\frac{0±2\sqrt{1994}}{2}$$

Now solve the equation h=\frac{0±2\sqrt{1994}}{2} when ± is plus.

$$h=\sqrt{1994}$$

Now solve the equation h=\frac{0±2\sqrt{1994}}{2} when ± is minus.

$$h=-\sqrt{1994}$$

The equation is now solved.

$$h=\sqrt{1994} h=-\sqrt{1994}$$