Solve n^2/2=1

$$\frac { n ^ { 2 } } { 2 } = 1$$

Solve for n

$$n=\sqrt{2}\approx 1.414213562$$

$$n=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Multiply both sides by 2.

$$n^{2}=2$$

Take the square root of both sides of the equation.

$$n=\sqrt{2} n=-\sqrt{2}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$n^{2}=2$$

Subtract 2 from both sides.

$$n^{2}-2=0$$

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

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

Square 0.

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

Multiply -4 times -2.

$$n=\frac{0±\sqrt{8}}{2}$$

Take the square root of 8.

$$n=\frac{0±2\sqrt{2}}{2}$$

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

$$n=\sqrt{2}$$

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

$$n=-\sqrt{2}$$

The equation is now solved.

$$n=\sqrt{2} n=-\sqrt{2}$$