Solve 3^2+6^2=c^2

$$3 ^ { 2 } + 6 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=3\sqrt{5}\approx 6.708203932$$

$$c=-3\sqrt{5}\approx -6.708203932$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$9+6^{2}=c^{2}$$

Calculate 6 to the power of 2 and get 36.

$$9+36=c^{2}$$

Add 9 and 36 to get 45.

$$45=c^{2}$$

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

$$c^{2}=45$$

Take the square root of both sides of the equation.

$$c=3\sqrt{5} c=-3\sqrt{5}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$9+6^{2}=c^{2}$$

Calculate 6 to the power of 2 and get 36.

$$9+36=c^{2}$$

Add 9 and 36 to get 45.

$$45=c^{2}$$

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

$$c^{2}=45$$

Subtract 45 from both sides.

$$c^{2}-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-45\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-45\right)}}{2}$$

Multiply -4 times -45.

$$c=\frac{0±\sqrt{180}}{2}$$

Take the square root of 180.

$$c=\frac{0±6\sqrt{5}}{2}$$

Now solve the equation c=\frac{0±6\sqrt{5}}{2} when ± is plus.

$$c=3\sqrt{5}$$

Now solve the equation c=\frac{0±6\sqrt{5}}{2} when ± is minus.

$$c=-3\sqrt{5}$$

The equation is now solved.

$$c=3\sqrt{5} c=-3\sqrt{5}$$