Solve p=sqrt{a/pix}

$$p = \sqrt { \frac { a } { \pi x } }$$

Solve for a

$$a=\pi xp^{2}$$

$$p\geq 0\text{ and }x\neq 0$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{\frac{a}{\pi x}}=p$$

Square both sides of the equation.

$$\frac{1}{\pi x}a=p^{2}$$

Divide both sides by \pi ^{-1}x^{-1}.

$$\frac{\frac{1}{\pi x}a\pi x}{1}=\frac{p^{2}\pi x}{1}$$

Dividing by \pi ^{-1}x^{-1} undoes the multiplication by \pi ^{-1}x^{-1}.

$$a=\frac{p^{2}\pi x}{1}$$

Divide p^{2} by \pi ^{-1}x^{-1}.

$$a=\pi xp^{2}$$

Solve for a (complex solution)

$$a=\pi xp^{2}$$

$$x\neq 0\text{ and }\left(p=0\text{ or }arg(p)<\pi \right)$$

Solve for p (complex solution)

$$p=\sqrt{\frac{a}{\pi x}}$$

$$x\neq 0$$

Solve for p

$$p=\sqrt{\frac{a}{\pi x}}$$

$$\left(a\geq 0\text{ and }x>0\right)\text{ or }\left(a\leq 0\text{ and }x<0\right)$$