Solve sqrt{3}t^2=-3

$$\sqrt { 3 } t ^ { 2 } = - 3$$

Solve for t

$$t=-\sqrt[4]{3}i\approx -0-1.316074013i$$

$$t=\sqrt[4]{3}i\approx 1.316074013i$$

Steps by Finding Square Root

Dividing by \sqrt{3} undoes the multiplication by \sqrt{3}.

$$t^{2}=-\frac{3}{\sqrt{3}}$$

Divide -3 by \sqrt{3}.

$$t^{2}=-\sqrt{3}$$

Take the square root of both sides of the equation.

$$t=\sqrt[4]{3}i t=-\sqrt[4]{3}i$$

Steps Using the Quadratic Formula

Add 3 to both sides.

$$\sqrt{3}t^{2}+3=0$$

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

$$t=\frac{0±\sqrt{0^{2}-4\sqrt{3}\times 3}}{2\sqrt{3}}$$

Square 0.

$$t=\frac{0±\sqrt{-4\sqrt{3}\times 3}}{2\sqrt{3}}$$

Multiply -4 times \sqrt{3}.

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

Multiply -4\sqrt{3} times 3.

$$t=\frac{0±\sqrt{-12\sqrt{3}}}{2\sqrt{3}}$$

Take the square root of -12\sqrt{3}.

$$t=\frac{0±2\times 3^{\frac{3}{4}}i}{2\sqrt{3}}$$

Now solve the equation t=\frac{0±2\times 3^{\frac{3}{4}}i}{2\sqrt{3}} when ± is plus.

$$t=\sqrt[4]{3}i$$

Now solve the equation t=\frac{0±2\times 3^{\frac{3}{4}}i}{2\sqrt{3}} when ± is minus.

$$t=-\sqrt[4]{3}i$$

The equation is now solved.

$$t=\sqrt[4]{3}i t=-\sqrt[4]{3}i$$