Solve c^2=2^2+3^2

$$c ^ { 2 } = 2 ^ { 2 } + 3 ^ { 2 }$$

Solve for c

$$c=\sqrt{13}\approx 3.605551275$$

$$c=-\sqrt{13}\approx -3.605551275$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

$$c^{2}=4+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$c^{2}=4+9$$

Add 4 and 9 to get 13.

$$c^{2}=13$$

Take the square root of both sides of the equation.

$$c=\sqrt{13} c=-\sqrt{13}$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

$$c^{2}=4+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$c^{2}=4+9$$

Add 4 and 9 to get 13.

$$c^{2}=13$$

Subtract 13 from both sides.

$$c^{2}-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-13\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-13\right)}}{2}$$

Multiply -4 times -13.

$$c=\frac{0±\sqrt{52}}{2}$$

Take the square root of 52.

$$c=\frac{0±2\sqrt{13}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{13}}{2} when ± is plus.

$$c=\sqrt{13}$$

Now solve the equation c=\frac{0±2\sqrt{13}}{2} when ± is minus.

$$c=-\sqrt{13}$$

The equation is now solved.

$$c=\sqrt{13} c=-\sqrt{13}$$