Solve 47/4700*(sqrt{400/400000})*(x*100)=1

$$\frac{ 47 }{ 4700 } \times ( \sqrt{ \frac{ 400 }{ 400000 } } ) \times (x \times 100)=1$$

Solve for x

$$x=10\sqrt{10}\approx 31.622776602$$

Steps for Solving Linear Equation

Reduce the fraction \frac{47}{4700} to lowest terms by extracting and canceling out 47.

$$\frac{1}{100}\sqrt{\frac{400}{400000}}x\times 100=1$$

Reduce the fraction \frac{400}{400000} to lowest terms by extracting and canceling out 400.

$$\frac{1}{100}\sqrt{\frac{1}{1000}}x\times 100=1$$

Rewrite the square root of the division \sqrt{\frac{1}{1000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{1000}}.

$$\frac{1}{100}\times \frac{\sqrt{1}}{\sqrt{1000}}x\times 100=1$$

Calculate the square root of 1 and get 1.

$$\frac{1}{100}\times \frac{1}{\sqrt{1000}}x\times 100=1$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$\frac{1}{100}\times \frac{1}{10\sqrt{10}}x\times 100=1$$

Rationalize the denominator of \frac{1}{10\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{1}{100}\times \frac{\sqrt{10}}{10\left(\sqrt{10}\right)^{2}}x\times 100=1$$

The square of \sqrt{10} is 10.

$$\frac{1}{100}\times \frac{\sqrt{10}}{10\times 10}x\times 100=1$$

Multiply 10 and 10 to get 100.

$$\frac{1}{100}\times \frac{\sqrt{10}}{100}x\times 100=1$$

Cancel out 100 and 100.

$$\frac{\sqrt{10}}{100}x=1$$

Express \frac{\sqrt{10}}{100}x as a single fraction.

$$\frac{\sqrt{10}x}{100}=1$$

Multiply both sides by 100.

$$\sqrt{10}x=100$$

Divide both sides by \sqrt{10}.

$$\frac{\sqrt{10}x}{\sqrt{10}}=\frac{100}{\sqrt{10}}$$

Dividing by \sqrt{10} undoes the multiplication by \sqrt{10}.

$$x=\frac{100}{\sqrt{10}}$$

Divide 100 by \sqrt{10}.

$$x=10\sqrt{10}$$