Solve T^2/m=4sqrt{49/n}

$$\frac { T ^ { 2 } } { m } = 4 \sqrt { \frac { 49 } { n } }$$

Solve for m

$$m=\frac{\sqrt{n}T^{2}}{28}$$

$$T\neq 0\text{ and }n>0$$

Steps for Solving Linear Equation

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

$$T^{2}=4\sqrt{\frac{49}{n}}m$$

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

$$4\sqrt{\frac{49}{n}}m=T^{2}$$

Divide both sides by 4\sqrt{49n^{-1}}.

$$\frac{4\sqrt{\frac{49}{n}}m}{4\sqrt{\frac{49}{n}}}=\frac{T^{2}}{4\sqrt{\frac{49}{n}}}$$

Dividing by 4\sqrt{49n^{-1}} undoes the multiplication by 4\sqrt{49n^{-1}}.

$$m=\frac{T^{2}}{4\sqrt{\frac{49}{n}}}$$

Divide T^{2} by 4\sqrt{49n^{-1}}.

$$m=\frac{\sqrt{n}T^{2}}{28}$$

Variable m cannot be equal to 0.

$$m=\frac{\sqrt{n}T^{2}}{28}\text{, }m\neq 0$$

Solve for T

$$T=\frac{2\sqrt{7m}}{\sqrt[4]{n}}$$

$$T=-\frac{2\sqrt{7m}}{\sqrt[4]{n}}\text{, }n>0\text{ and }m>0$$