Solve 1/4sqrt{4x}=y

$$\frac{ 1 }{ 4 } \sqrt{ 4x } =y$$

Solve for x

$$x=4y^{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

Multiply both sides by 4.

$$\frac{\frac{1}{4}\sqrt{4x}}{\frac{1}{4}}=\frac{y}{\frac{1}{4}}$$

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

$$\sqrt{4x}=\frac{y}{\frac{1}{4}}$$

Divide y by \frac{1}{4} by multiplying y by the reciprocal of \frac{1}{4}.

$$\sqrt{4x}=4y$$

Square both sides of the equation.

$$4x=16y^{2}$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{16y^{2}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{16y^{2}}{4}$$

Divide 16y^{2} by 4.

$$x=4y^{2}$$

Solve for x (complex solution)

$$x=4y^{2}$$

$$arg(y)<\pi \text{ or }y=0$$

Solve for y (complex solution)

$$y=\frac{\sqrt{x}}{2}$$

Solve for y

$$y=\frac{\sqrt{x}}{2}$$

$$x\geq 0$$