Solve sqrt{5v}=v

$$\sqrt { 5 v } = v$$

Solve for v

$$v=5$$

$$v=0$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{5v}\right)^{2}=v^{2}$$

Calculate \sqrt{5v} to the power of 2 and get 5v.

$$5v=v^{2}$$

Subtract v^{2} from both sides.

$$5v-v^{2}=0$$

Factor out v.

$$v\left(5-v\right)=0$$

To find equation solutions, solve v=0 and 5-v=0.

$$v=0 v=5$$

Substitute 0 for v in the equation \sqrt{5v}=v.

$$\sqrt{5\times 0}=0$$

Simplify. The value v=0 satisfies the equation.

$$0=0$$

Substitute 5 for v in the equation \sqrt{5v}=v.

$$\sqrt{5\times 5}=5$$

Simplify. The value v=5 satisfies the equation.

$$5=5$$

List all solutions of \sqrt{5v}=v.

$$v=0 v=5$$