Solve sqrt{a^2}=(sqrt{a})

$$\sqrt { a ^ { 2 } } = ( \sqrt { a } )$$

Solve for a

$$a=0$$

$$a=1$$

Solution Steps

Square both sides of the equation.

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

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

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

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

$$a^{2}=a$$

Subtract a from both sides.

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

Factor out a.

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

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

$$a=0 a=1$$

Substitute 0 for a in the equation \sqrt{a^{2}}=\sqrt{a}.

$$\sqrt{0^{2}}=\sqrt{0}$$

Simplify. The value a=0 satisfies the equation.

$$0=0$$

Substitute 1 for a in the equation \sqrt{a^{2}}=\sqrt{a}.

$$\sqrt{1^{2}}=\sqrt{1}$$

Simplify. The value a=1 satisfies the equation.

$$1=1$$

List all solutions of \sqrt{a^{2}}=\sqrt{a}.

$$a=0 a=1$$