Solve xsqrt{1}=sqrt{x}

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

Solve for x

$$x=0$$

$$x=1$$

Solution Steps

Square both sides of the equation.

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

Calculate the square root of 1 and get 1.

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

Expand \left(x\times 1\right)^{2}.

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

Calculate 1 to the power of 2 and get 1.

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

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

$$x^{2}\times 1=x$$

Reorder the terms.

$$x^{2}=x$$

Subtract x from both sides.

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

Factor out x.

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

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

$$x=0 x=1$$

Substitute 0 for x in the equation x\sqrt{1}=\sqrt{x}.

$$0\sqrt{1}=\sqrt{0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 1 for x in the equation x\sqrt{1}=\sqrt{x}.

$$1\sqrt{1}=\sqrt{1}$$

Simplify. The value x=1 satisfies the equation.

$$1=1$$

List all solutions of \sqrt{1}x=\sqrt{x}.

$$x=0 x=1$$