Solve sqrt{2x}-sqrt{x}=0

$$\sqrt{ 2x } - \sqrt{ x } =0$$

Solve for x

$$x=0$$

Solution Steps

Subtract -\sqrt{x} from both sides of the equation.

$$\sqrt{2x}=\sqrt{x}$$

Square both sides of the equation.

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

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

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

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

$$2x=x$$

Subtract x from both sides.

$$2x-x=0$$

Combine 2x and -x to get x.

$$x=0$$

Substitute 0 for x in the equation \sqrt{2x}-\sqrt{x}=0.

$$\sqrt{2\times 0}-\sqrt{0}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Equation \sqrt{2x}=\sqrt{x} has a unique solution.

$$x=0$$