Solve x^248=1

$${ x }^{ 2 } 48=1$$

Solve for x

$$x=\frac{\sqrt{3}}{12}\approx 0.144337567$$

$$x=-\frac{\sqrt{3}}{12}\approx -0.144337567$$

Steps by Finding Square Root

Divide both sides by 48.

$$x^{2}=\frac{1}{48}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3}}{12} x=-\frac{\sqrt{3}}{12}$$

Steps Using the Quadratic Formula

Divide both sides by 48.

$$x^{2}=\frac{1}{48}$$

Subtract \frac{1}{48} from both sides.

$$x^{2}-\frac{1}{48}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{48} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{48}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{48}\right)}}{2}$$

Multiply -4 times -\frac{1}{48}.

$$x=\frac{0±\sqrt{\frac{1}{12}}}{2}$$

Take the square root of \frac{1}{12}.

$$x=\frac{0±\frac{\sqrt{3}}{6}}{2}$$

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

$$x=\frac{\sqrt{3}}{12}$$

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

$$x=-\frac{\sqrt{3}}{12}$$

The equation is now solved.

$$x=\frac{\sqrt{3}}{12} x=-\frac{\sqrt{3}}{12}$$