Solve {left(sqrt{x}right)}^2=sqrt{x^}

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

Solve for x

$$x=0$$

$$x=1$$

Solution Steps

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

$$x=\sqrt{x^{1}}$$

Calculate x to the power of 1 and get x.

$$x=\sqrt{x}$$

Subtract \sqrt{x} from both sides.

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

Subtract x from both sides of the equation.

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

Cancel out -1 on both sides.

$$\sqrt{x}=x$$

Square both sides of the equation.

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

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

$$x=x^{2}$$

Subtract x^{2} from both sides.

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

Factor out x.

$$x\left(1-x\right)=0$$

To find equation solutions, solve x=0 and 1-x=0.

$$x=0 x=1$$

Substitute 0 for x in the equation \left(\sqrt{x}\right)^{2}=\sqrt{x^{1}}.

$$\left(\sqrt{0}\right)^{2}=\sqrt{0^{1}}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 1 for x in the equation \left(\sqrt{x}\right)^{2}=\sqrt{x^{1}}.

$$\left(\sqrt{1}\right)^{2}=\sqrt{1^{1}}$$

Simplify. The value x=1 satisfies the equation.

$$1=1$$

List all solutions of \sqrt{x}=x.

$$x=0 x=1$$