Solve R^2pi=30

$$R ^ { 2 } \pi = 30$$

Solve for R

$$R=\sqrt{\frac{30}{\pi }}\approx 3.090193616$$

$$R=-\sqrt{\frac{30}{\pi }}\approx -3.090193616$$

Steps by Finding Square Root

Divide both sides by \pi .

$$\frac{\pi R^{2}}{\pi }=\frac{30}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$R^{2}=\frac{30}{\pi }$$

Take the square root of both sides of the equation.

$$R=\frac{30}{\sqrt{30\pi }} R=-\frac{30}{\sqrt{30\pi }}$$

Steps Using the Quadratic Formula

Subtract 30 from both sides.

$$R^{2}\pi -30=0$$

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.

$$\pi R^{2}-30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{0±\sqrt{0^{2}-4\pi \left(-30\right)}}{2\pi }$$

Square 0.

$$R=\frac{0±\sqrt{-4\pi \left(-30\right)}}{2\pi }$$

Multiply -4 times \pi .

$$R=\frac{0±\sqrt{\left(-4\pi \right)\left(-30\right)}}{2\pi }$$

Multiply -4\pi times -30.

$$R=\frac{0±\sqrt{120\pi }}{2\pi }$$

Take the square root of 120\pi .

$$R=\frac{0±2\sqrt{30\pi }}{2\pi }$$

Now solve the equation R=\frac{0±2\sqrt{30\pi }}{2\pi } when ± is plus.

$$R=\frac{30}{\sqrt{30\pi }}$$

Now solve the equation R=\frac{0±2\sqrt{30\pi }}{2\pi } when ± is minus.

$$R=-\frac{30}{\sqrt{30\pi }}$$

The equation is now solved.

$$R=\frac{30}{\sqrt{30\pi }} R=-\frac{30}{\sqrt{30\pi }}$$