Solve sqrt{4a}=2a

$$\sqrt { 4 a } = 2 a$$

Solve for a

$$a=1$$

$$a=0$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{4a}\right)^{2}=\left(2a\right)^{2}$$

Calculate \sqrt{4a} to the power of 2 and get 4a.

$$4a=\left(2a\right)^{2}$$

Expand \left(2a\right)^{2}.

$$4a=2^{2}a^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4a=4a^{2}$$

Cancel out 4 on both sides.

$$a=a^{2}$$

Subtract a^{2} from both sides.

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

Factor out a.

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

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

$$a=0 a=1$$

Substitute 0 for a in the equation \sqrt{4a}=2a.

$$\sqrt{4\times 0}=2\times 0$$

Simplify. The value a=0 satisfies the equation.

$$0=0$$

Substitute 1 for a in the equation \sqrt{4a}=2a.

$$\sqrt{4\times 1}=2\times 1$$

Simplify. The value a=1 satisfies the equation.

$$2=2$$

List all solutions of \sqrt{4a}=2a.

$$a=0 a=1$$