Solve 2xsqrt{18811/89}

$$2 x \sqrt { \frac { 18811 } { 89 } }$$

Evaluate

$$\frac{2\sqrt{1674179}x}{89}$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{18811}{89}} as the division of square roots \frac{\sqrt{18811}}{\sqrt{89}}.

$$2x\times \frac{\sqrt{18811}}{\sqrt{89}}$$

Rationalize the denominator of \frac{\sqrt{18811}}{\sqrt{89}} by multiplying numerator and denominator by \sqrt{89}.

$$2x\times \frac{\sqrt{18811}\sqrt{89}}{\left(\sqrt{89}\right)^{2}}$$

The square of \sqrt{89} is 89.

$$2x\times \frac{\sqrt{18811}\sqrt{89}}{89}$$

To multiply \sqrt{18811} and \sqrt{89}, multiply the numbers under the square root.

$$2x\times \frac{\sqrt{1674179}}{89}$$

Express 2\times \frac{\sqrt{1674179}}{89} as a single fraction.

$$\frac{2\sqrt{1674179}}{89}x$$

Express \frac{2\sqrt{1674179}}{89}x as a single fraction.

$$\frac{2\sqrt{1674179}x}{89}$$

Differentiate w.r.t. x

$$\frac{2 \sqrt{1674179}}{89} = 29.076420038360826$$