Solve sqrt{u}=sqrt{sqrt{u}}

$$\sqrt { u } = \sqrt { \sqrt { u } }$$

Solve for u

$$u=0$$

$$u=1$$

Solution Steps

Square both sides of the equation.

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

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

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

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

$$u=\sqrt{u}$$

Square both sides of the equation.

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

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

$$u^{2}=u$$

Subtract u from both sides.

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

Factor out u.

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

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

$$u=0 u=1$$

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

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

Simplify. The value u=0 satisfies the equation.

$$0=0$$

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

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

Simplify. The value u=1 satisfies the equation.

$$1=1$$

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

$$u=0 u=1$$