Solve c*8/4sqrt{5/3}

$$c \cdot \frac { 8 } { 4 } \sqrt { \frac { 5 } { 3 } }$$

Evaluate

$$\frac{2\sqrt{15}c}{3}$$

Solution Steps

Divide 8 by 4 to get 2.

$$c\times 2\sqrt{\frac{5}{3}}$$

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

$$c\times 2\times \frac{\sqrt{5}}{\sqrt{3}}$$

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

$$c\times 2\times \frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$c\times 2\times \frac{\sqrt{5}\sqrt{3}}{3}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$c\times 2\times \frac{\sqrt{15}}{3}$$

Express c\times \frac{\sqrt{15}}{3} as a single fraction.

$$\frac{c\sqrt{15}}{3}\times 2$$

Express \frac{c\sqrt{15}}{3}\times 2 as a single fraction.

$$\frac{c\sqrt{15}\times 2}{3}$$

Differentiate w.r.t. c

$$\frac{2 \sqrt{15}}{3} = 2.581988897471611$$