Solve 3^2+5^2=c^2

$$3 ^ { 2 } + 5 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=\sqrt{34}\approx 5.830951895$$

$$c=-\sqrt{34}\approx -5.830951895$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$9+5^{2}=c^{2}$$

Calculate 5 to the power of 2 and get 25.

$$9+25=c^{2}$$

Add 9 and 25 to get 34.

$$34=c^{2}$$

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

$$c^{2}=34$$

Take the square root of both sides of the equation.

$$c=\sqrt{34} c=-\sqrt{34}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$9+5^{2}=c^{2}$$

Calculate 5 to the power of 2 and get 25.

$$9+25=c^{2}$$

Add 9 and 25 to get 34.

$$34=c^{2}$$

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

$$c^{2}=34$$

Subtract 34 from both sides.

$$c^{2}-34=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -34 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-34\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-34\right)}}{2}$$

Multiply -4 times -34.

$$c=\frac{0±\sqrt{136}}{2}$$

Take the square root of 136.

$$c=\frac{0±2\sqrt{34}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{34}}{2} when ± is plus.

$$c=\sqrt{34}$$

Now solve the equation c=\frac{0±2\sqrt{34}}{2} when ± is minus.

$$c=-\sqrt{34}$$

The equation is now solved.

$$c=\sqrt{34} c=-\sqrt{34}$$