Solve 1/3=t^2

$$\frac { 1 } { 3 } = t ^ { 2 }$$

Solve for t

$$t=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$t=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps by Finding Square Root

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

$$t^{2}=\frac{1}{3}$$

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{3}}{3} t=-\frac{\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

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

$$t^{2}=\frac{1}{3}$$

Subtract \frac{1}{3} from both sides.

$$t^{2}-\frac{1}{3}=0$$

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

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{3}\right)}}{2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{1}{3}\right)}}{2}$$

Multiply -4 times -\frac{1}{3}.

$$t=\frac{0±\sqrt{\frac{4}{3}}}{2}$$

Take the square root of \frac{4}{3}.

$$t=\frac{0±\frac{2\sqrt{3}}{3}}{2}$$

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

$$t=\frac{\sqrt{3}}{3}$$

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

$$t=-\frac{\sqrt{3}}{3}$$

The equation is now solved.

$$t=\frac{\sqrt{3}}{3} t=-\frac{\sqrt{3}}{3}$$