Solve a^2-3=0

$$a ^ { 2 } - 3 = 0$$

Solve for a

$$a=\sqrt{3}\approx 1.732050808$$

$$a=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Add 3 to both sides. Anything plus zero gives itself.

$$a^{2}=3$$

Take the square root of both sides of the equation.

$$a=\sqrt{3} a=-\sqrt{3}$$

Steps Using the Quadratic Formula

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.

$$a^{2}-3=0$$

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

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

Square 0.

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

Multiply -4 times -3.

$$a=\frac{0±\sqrt{12}}{2}$$

Take the square root of 12.

$$a=\frac{0±2\sqrt{3}}{2}$$

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

$$a=\sqrt{3}$$

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

$$a=-\sqrt{3}$$

The equation is now solved.

$$a=\sqrt{3} a=-\sqrt{3}$$