Solve 2^2+4^2=c^2

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

Solve for c

$$c=2\sqrt{5}\approx 4.472135955$$

$$c=-2\sqrt{5}\approx -4.472135955$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

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

Calculate 4 to the power of 2 and get 16.

$$4+16=c^{2}$$

Add 4 and 16 to get 20.

$$20=c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$c^{2}=20$$

Take the square root of both sides of the equation.

$$c=2\sqrt{5} c=-2\sqrt{5}$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

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

Calculate 4 to the power of 2 and get 16.

$$4+16=c^{2}$$

Add 4 and 16 to get 20.

$$20=c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$c^{2}=20$$

Subtract 20 from both sides.

$$c^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-20\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-20\right)}}{2}$$

Multiply -4 times -20.

$$c=\frac{0±\sqrt{80}}{2}$$

Take the square root of 80.

$$c=\frac{0±4\sqrt{5}}{2}$$

Now solve the equation c=\frac{0±4\sqrt{5}}{2} when ± is plus.

$$c=2\sqrt{5}$$

Now solve the equation c=\frac{0±4\sqrt{5}}{2} when ± is minus.

$$c=-2\sqrt{5}$$

The equation is now solved.

$$c=2\sqrt{5} c=-2\sqrt{5}$$