Solve sqrt{x}=8x

$$\sqrt { x } = 8 x$$

Solve for x

$$x=0$$

$$x=\frac{1}{64}=0.015625$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x}\right)^{2}=\left(8x\right)^{2}$$

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

$$x=\left(8x\right)^{2}$$

Expand \left(8x\right)^{2}.

$$x=8^{2}x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$x=64x^{2}$$

Subtract 64x^{2} from both sides.

$$x-64x^{2}=0$$

Factor out x.

$$x\left(1-64x\right)=0$$

To find equation solutions, solve x=0 and 1-64x=0.

$$x=0 x=\frac{1}{64}$$

Substitute 0 for x in the equation \sqrt{x}=8x.

$$\sqrt{0}=8\times 0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{1}{64} for x in the equation \sqrt{x}=8x.

$$\sqrt{\frac{1}{64}}=8\times \frac{1}{64}$$

Simplify. The value x=\frac{1}{64} satisfies the equation.

$$\frac{1}{8}=\frac{1}{8}$$

List all solutions of \sqrt{x}=8x.

$$x=0 x=\frac{1}{64}$$