Solve c^2=13+15^2

$$c ^ { 2 } = 13 + 15 ^ { 2 }$$

Solve for c

$$c=\sqrt{238}\approx 15.427248621$$

$$c=-\sqrt{238}\approx -15.427248621$$

Steps by Finding Square Root

Calculate 15 to the power of 2 and get 225.

$$c^{2}=13+225$$

Add 13 and 225 to get 238.

$$c^{2}=238$$

Take the square root of both sides of the equation.

$$c=\sqrt{238} c=-\sqrt{238}$$

Steps Using the Quadratic Formula

Calculate 15 to the power of 2 and get 225.

$$c^{2}=13+225$$

Add 13 and 225 to get 238.

$$c^{2}=238$$

Subtract 238 from both sides.

$$c^{2}-238=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -238 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-238\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-238\right)}}{2}$$

Multiply -4 times -238.

$$c=\frac{0±\sqrt{952}}{2}$$

Take the square root of 952.

$$c=\frac{0±2\sqrt{238}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{238}}{2} when ± is plus.

$$c=\sqrt{238}$$

Now solve the equation c=\frac{0±2\sqrt{238}}{2} when ± is minus.

$$c=-\sqrt{238}$$

The equation is now solved.

$$c=\sqrt{238} c=-\sqrt{238}$$