Solve rH2/8mL/s=sqrt{1.44/0.09}

$$\frac { rH 2 } { 8 mL / s } = \sqrt { \frac { 1.44 } { 0.09 } }$$

Solve for H_2

$$H_{2}=\frac{32Lm}{rs}$$

$$s\neq 0\text{ and }r\neq 0\text{ and }m\neq 0\text{ and }L\neq 0$$

Steps for Solving Linear Equation

Divide rH_{2} by \frac{8mL}{s} by multiplying rH_{2} by the reciprocal of \frac{8mL}{s}.

$$\frac{rH_{2}s}{8mL}=\sqrt{\frac{1.44}{0.09}}$$

Expand \frac{1.44}{0.09} by multiplying both numerator and the denominator by 100.

$$\frac{rH_{2}s}{8mL}=\sqrt{\frac{144}{9}}$$

Divide 144 by 9 to get 16.

$$\frac{rH_{2}s}{8mL}=\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$\frac{rH_{2}s}{8mL}=4$$

Multiply both sides of the equation by 8Lm.

$$rH_{2}s=32Lm$$

The equation is in standard form.

$$rsH_{2}=32Lm$$

Divide both sides by rs.

$$\frac{rsH_{2}}{rs}=\frac{32Lm}{rs}$$

Dividing by rs undoes the multiplication by rs.

$$H_{2}=\frac{32Lm}{rs}$$

Solve for L

$$L=\frac{H_{2}rs}{32m}$$

$$s\neq 0\text{ and }H_{2}\neq 0\text{ and }r\neq 0\text{ and }m\neq 0$$

Steps for Solving Linear Equation

Divide rH_{2} by \frac{8mL}{s} by multiplying rH_{2} by the reciprocal of \frac{8mL}{s}.

$$\frac{rH_{2}s}{8mL}=\sqrt{\frac{1.44}{0.09}}$$

Expand \frac{1.44}{0.09} by multiplying both numerator and the denominator by 100.

$$\frac{rH_{2}s}{8mL}=\sqrt{\frac{144}{9}}$$

Divide 144 by 9 to get 16.

$$\frac{rH_{2}s}{8mL}=\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$\frac{rH_{2}s}{8mL}=4$$

Variable L cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8Lm.

$$rH_{2}s=32Lm$$

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

$$32Lm=rH_{2}s$$

The equation is in standard form.

$$32mL=H_{2}rs$$

Divide both sides by 32m.

$$\frac{32mL}{32m}=\frac{H_{2}rs}{32m}$$

Dividing by 32m undoes the multiplication by 32m.

$$L=\frac{H_{2}rs}{32m}$$

Variable L cannot be equal to 0.

$$L=\frac{H_{2}rs}{32m}\text{, }L\neq 0$$