Solve sqrt{1/20(19/20)95000/500(500+9500)}

$$\sqrt { \frac { 1 } { 20 } ( \frac { 19 } { 20 } ) \frac { 95000 } { 500 ( 500 + 9500 ) } }$$

Evaluate

$$\frac{19\sqrt{10}}{2000}\approx 0.030041638$$

Solution Steps

Multiply \frac{1}{20} times \frac{19}{20} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{1\times 19}{20\times 20}\times \frac{95000}{500\left(500+9500\right)}}$$

Do the multiplications in the fraction \frac{1\times 19}{20\times 20}.

$$\sqrt{\frac{19}{400}\times \frac{95000}{500\left(500+9500\right)}}$$

Add 500 and 9500 to get 10000.

$$\sqrt{\frac{19}{400}\times \frac{95000}{500\times 10000}}$$

Multiply 500 and 10000 to get 5000000.

$$\sqrt{\frac{19}{400}\times \frac{95000}{5000000}}$$

Reduce the fraction \frac{95000}{5000000} to lowest terms by extracting and canceling out 5000.

$$\sqrt{\frac{19}{400}\times \frac{19}{1000}}$$

Multiply \frac{19}{400} times \frac{19}{1000} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{19\times 19}{400\times 1000}}$$

Do the multiplications in the fraction \frac{19\times 19}{400\times 1000}.

$$\sqrt{\frac{361}{400000}}$$

Rewrite the square root of the division \sqrt{\frac{361}{400000}} as the division of square roots \frac{\sqrt{361}}{\sqrt{400000}}.

$$\frac{\sqrt{361}}{\sqrt{400000}}$$

Calculate the square root of 361 and get 19.

$$\frac{19}{\sqrt{400000}}$$

Factor 400000=200^{2}\times 10. Rewrite the square root of the product \sqrt{200^{2}\times 10} as the product of square roots \sqrt{200^{2}}\sqrt{10}. Take the square root of 200^{2}.

$$\frac{19}{200\sqrt{10}}$$

Rationalize the denominator of \frac{19}{200\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{19\sqrt{10}}{200\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{19\sqrt{10}}{200\times 10}$$

Multiply 200 and 10 to get 2000.

$$\frac{19\sqrt{10}}{2000}$$