Solve r^2=1-3/9

$$r ^ { 2 } = 1 - \frac { 3 } { 9 }$$

Solve for r

$$r=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$r=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps by Finding Square Root

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$r^{2}=1-\frac{1}{3}$$

Subtract \frac{1}{3} from 1 to get \frac{2}{3}.

$$r^{2}=\frac{2}{3}$$

Take the square root of both sides of the equation.

$$r=\frac{\sqrt{6}}{3} r=-\frac{\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$r^{2}=1-\frac{1}{3}$$

Subtract \frac{1}{3} from 1 to get \frac{2}{3}.

$$r^{2}=\frac{2}{3}$$

Subtract \frac{2}{3} from both sides.

$$r^{2}-\frac{2}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{2}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{2}{3}\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-\frac{2}{3}\right)}}{2}$$

Multiply -4 times -\frac{2}{3}.

$$r=\frac{0±\sqrt{\frac{8}{3}}}{2}$$

Take the square root of \frac{8}{3}.

$$r=\frac{0±\frac{2\sqrt{6}}{3}}{2}$$

Now solve the equation r=\frac{0±\frac{2\sqrt{6}}{3}}{2} when ± is plus.

$$r=\frac{\sqrt{6}}{3}$$

Now solve the equation r=\frac{0±\frac{2\sqrt{6}}{3}}{2} when ± is minus.

$$r=-\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$r=\frac{\sqrt{6}}{3} r=-\frac{\sqrt{6}}{3}$$