Solve 7=2pisqrt{l/y}

$$7 = 2 \pi \sqrt { \frac { l } { y } }$$

Solve for l

$$l=\frac{49y}{4\pi ^{2}}$$

$$y\neq 0$$

Steps for Solving Radical Equations

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

$$2\pi \sqrt{\frac{l}{y}}=7$$

Divide both sides by 2\pi .

$$\frac{2\pi \sqrt{\frac{1}{y}l}}{2\pi }=\frac{7}{2\pi }$$

Dividing by 2\pi undoes the multiplication by 2\pi .

$$\sqrt{\frac{1}{y}l}=\frac{7}{2\pi }$$

Square both sides of the equation.

$$\frac{1}{y}l=\frac{49}{4\pi ^{2}}$$

Divide both sides by y^{-1}.

$$\frac{\frac{1}{y}ly}{1}=\frac{49}{4\pi ^{2}\times \frac{1}{y}}$$

Dividing by y^{-1} undoes the multiplication by y^{-1}.

$$l=\frac{49}{4\pi ^{2}\times \frac{1}{y}}$$

Divide \frac{49}{4\pi ^{2}} by y^{-1}.

$$l=\frac{49y}{4\pi ^{2}}$$

Solve for y

$$y=\frac{4\pi ^{2}l}{49}$$

$$l\neq 0$$