Solve c^2=13^2+15^2

$$c ^ { 2 } = 13 ^ { 2 } + 15 ^ { 2 }$$

Solve for c

$$c=\sqrt{394}\approx 19.849433241$$

$$c=-\sqrt{394}\approx -19.849433241$$

Steps by Finding Square Root

Calculate 13 to the power of 2 and get 169.

$$c^{2}=169+15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$c^{2}=169+225$$

Add 169 and 225 to get 394.

$$c^{2}=394$$

Take the square root of both sides of the equation.

$$c=\sqrt{394} c=-\sqrt{394}$$

Steps Using the Quadratic Formula

Calculate 13 to the power of 2 and get 169.

$$c^{2}=169+15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$c^{2}=169+225$$

Add 169 and 225 to get 394.

$$c^{2}=394$$

Subtract 394 from both sides.

$$c^{2}-394=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -394 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-394\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-394\right)}}{2}$$

Multiply -4 times -394.

$$c=\frac{0±\sqrt{1576}}{2}$$

Take the square root of 1576.

$$c=\frac{0±2\sqrt{394}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{394}}{2} when ± is plus.

$$c=\sqrt{394}$$

Now solve the equation c=\frac{0±2\sqrt{394}}{2} when ± is minus.

$$c=-\sqrt{394}$$

The equation is now solved.

$$c=\sqrt{394} c=-\sqrt{394}$$