Solve r^2pi=2

$$r ^ { 2 } \pi = 2$$

Solve for r

$$r=\sqrt{\frac{2}{\pi }}\approx 0.797884561$$

$$r=-\sqrt{\frac{2}{\pi }}\approx -0.797884561$$

Steps by Finding Square Root

Divide both sides by \pi .

$$\frac{\pi r^{2}}{\pi }=\frac{2}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$r^{2}=\frac{2}{\pi }$$

Take the square root of both sides of the equation.

$$r=\frac{2}{\sqrt{2\pi }} r=-\frac{2}{\sqrt{2\pi }}$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$r^{2}\pi -2=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\pi r^{2}-2=0$$

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

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

Square 0.

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

Multiply -4 times \pi .

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

Multiply -4\pi times -2.

$$r=\frac{0±\sqrt{8\pi }}{2\pi }$$

Take the square root of 8\pi .

$$r=\frac{0±2\sqrt{2\pi }}{2\pi }$$

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

$$r=\frac{2}{\sqrt{2\pi }}$$

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

$$r=-\frac{2}{\sqrt{2\pi }}$$

The equation is now solved.

$$r=\frac{2}{\sqrt{2\pi }} r=-\frac{2}{\sqrt{2\pi }}$$