Solve 1/frac{1{3sqrt{5}}cm}

$$\frac { 1 } { \frac { 1 } { 3 \sqrt { 5 } } cm }$$

Evaluate

$$\frac{3\sqrt{5}}{cm}$$

Solution Steps

Rationalize the denominator of \frac{1}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{1}{\frac{\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}cm}$$

The square of \sqrt{5} is 5.

$$\frac{1}{\frac{\sqrt{5}}{3\times 5}cm}$$

Multiply 3 and 5 to get 15.

$$\frac{1}{\frac{\sqrt{5}}{15}cm}$$

Express \frac{\sqrt{5}}{15}c as a single fraction.

$$\frac{1}{\frac{\sqrt{5}c}{15}m}$$

Express \frac{\sqrt{5}c}{15}m as a single fraction.

$$\frac{1}{\frac{\sqrt{5}cm}{15}}$$

Divide 1 by \frac{\sqrt{5}cm}{15} by multiplying 1 by the reciprocal of \frac{\sqrt{5}cm}{15}.

$$\frac{15}{\sqrt{5}cm}$$

Rationalize the denominator of \frac{15}{\sqrt{5}cm} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{15\sqrt{5}}{\left(\sqrt{5}\right)^{2}cm}$$

The square of \sqrt{5} is 5.

$$\frac{15\sqrt{5}}{5cm}$$

Cancel out 5 in both numerator and denominator.

$$\frac{3\sqrt{5}}{cm}$$

Differentiate w.r.t. c

$$-\frac{3\sqrt{5}}{mc^{2}}$$