Solve 2xsqrt{18.811/89}

$$2 x \sqrt { \frac { 18.811 } { 89 } }$$

Evaluate

$$\frac{\sqrt{16741790}x}{4450}$$

Solution Steps

Expand \frac{18.811}{89} by multiplying both numerator and the denominator by 1000.

$$2x\sqrt{\frac{18811}{89000}}$$

Rewrite the square root of the division \sqrt{\frac{18811}{89000}} as the division of square roots \frac{\sqrt{18811}}{\sqrt{89000}}.

$$2x\times \frac{\sqrt{18811}}{\sqrt{89000}}$$

Factor 89000=10^{2}\times 890. Rewrite the square root of the product \sqrt{10^{2}\times 890} as the product of square roots \sqrt{10^{2}}\sqrt{890}. Take the square root of 10^{2}.

$$2x\times \frac{\sqrt{18811}}{10\sqrt{890}}$$

Rationalize the denominator of \frac{\sqrt{18811}}{10\sqrt{890}} by multiplying numerator and denominator by \sqrt{890}.

$$2x\times \frac{\sqrt{18811}\sqrt{890}}{10\left(\sqrt{890}\right)^{2}}$$

The square of \sqrt{890} is 890.

$$2x\times \frac{\sqrt{18811}\sqrt{890}}{10\times 890}$$

To multiply \sqrt{18811} and \sqrt{890}, multiply the numbers under the square root.

$$2x\times \frac{\sqrt{16741790}}{10\times 890}$$

Multiply 10 and 890 to get 8900.

$$2x\times \frac{\sqrt{16741790}}{8900}$$

Cancel out 8900, the greatest common factor in 2 and 8900.

$$\frac{\sqrt{16741790}}{4450}x$$

Express \frac{\sqrt{16741790}}{4450}x as a single fraction.

$$\frac{\sqrt{16741790}x}{4450}$$

Differentiate w.r.t. x

$$\frac{\sqrt{16741790}}{4450} = 0.9194771352498066$$