Solve 8^2+10^2=C^2

$$8 ^ { 2 } + 10 ^ { 2 } = C ^ { 2 }$$

Solve for C

$$C=2\sqrt{41}\approx 12.806248475$$

$$C=-2\sqrt{41}\approx -12.806248475$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$64+10^{2}=C^{2}$$

Calculate 10 to the power of 2 and get 100.

$$64+100=C^{2}$$

Add 64 and 100 to get 164.

$$164=C^{2}$$

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

$$C^{2}=164$$

Take the square root of both sides of the equation.

$$C=2\sqrt{41} C=-2\sqrt{41}$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$64+10^{2}=C^{2}$$

Calculate 10 to the power of 2 and get 100.

$$64+100=C^{2}$$

Add 64 and 100 to get 164.

$$164=C^{2}$$

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

$$C^{2}=164$$

Subtract 164 from both sides.

$$C^{2}-164=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -164 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$C=\frac{0±\sqrt{0^{2}-4\left(-164\right)}}{2}$$

Square 0.

$$C=\frac{0±\sqrt{-4\left(-164\right)}}{2}$$

Multiply -4 times -164.

$$C=\frac{0±\sqrt{656}}{2}$$

Take the square root of 656.

$$C=\frac{0±4\sqrt{41}}{2}$$

Now solve the equation C=\frac{0±4\sqrt{41}}{2} when ± is plus.

$$C=2\sqrt{41}$$

Now solve the equation C=\frac{0±4\sqrt{41}}{2} when ± is minus.

$$C=-2\sqrt{41}$$

The equation is now solved.

$$C=2\sqrt{41} C=-2\sqrt{41}$$