Solve operatorname{ce}sqrt{9/11}

$$\operatorname { ce } \sqrt { \frac { 9 } { 11 } }$$

Evaluate

$$\frac{3e\sqrt{11}c}{11}$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{9}{11}} as the division of square roots \frac{\sqrt{9}}{\sqrt{11}}.

$$ce\times \frac{\sqrt{9}}{\sqrt{11}}$$

Calculate the square root of 9 and get 3.

$$ce\times \frac{3}{\sqrt{11}}$$

Rationalize the denominator of \frac{3}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$ce\times \frac{3\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$ce\times \frac{3\sqrt{11}}{11}$$

Express c\times \frac{3\sqrt{11}}{11} as a single fraction.

$$\frac{c\times 3\sqrt{11}}{11}e$$

Express \frac{c\times 3\sqrt{11}}{11}e as a single fraction.

$$\frac{c\times 3\sqrt{11}e}{11}$$

Differentiate w.r.t. c

$$\frac{3e\sqrt{11}}{11}$$