Solve C^2=12^2+24^2

$$C ^ { 2 } = 12 ^ { 2 } + 24 ^ { 2 }$$

Solve for C

$$C=12\sqrt{5}\approx 26.83281573$$

$$C=-12\sqrt{5}\approx -26.83281573$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$C^{2}=144+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$C^{2}=144+576$$

Add 144 and 576 to get 720.

$$C^{2}=720$$

Take the square root of both sides of the equation.

$$C=12\sqrt{5} C=-12\sqrt{5}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$C^{2}=144+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$C^{2}=144+576$$

Add 144 and 576 to get 720.

$$C^{2}=720$$

Subtract 720 from both sides.

$$C^{2}-720=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -720 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$C=\frac{0±\sqrt{0^{2}-4\left(-720\right)}}{2}$$

Square 0.

$$C=\frac{0±\sqrt{-4\left(-720\right)}}{2}$$

Multiply -4 times -720.

$$C=\frac{0±\sqrt{2880}}{2}$$

Take the square root of 2880.

$$C=\frac{0±24\sqrt{5}}{2}$$

Now solve the equation C=\frac{0±24\sqrt{5}}{2} when ± is plus.

$$C=12\sqrt{5}$$

Now solve the equation C=\frac{0±24\sqrt{5}}{2} when ± is minus.

$$C=-12\sqrt{5}$$

The equation is now solved.

$$C=12\sqrt{5} C=-12\sqrt{5}$$