Solve lambda^2=2

$$\lambda ^ { 2 } = 2$$

Solve for λ

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

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

Steps by Finding Square Root

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$\lambda ^{2}-2=0$$

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}.

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

Square 0.

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

Multiply -4 times -2.

$$\lambda =\frac{0±\sqrt{8}}{2}$$

Take the square root of 8.

$$\lambda =\frac{0±2\sqrt{2}}{2}$$

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

$$\lambda =\sqrt{2}$$

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

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

The equation is now solved.

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