Solve 144/3,5*3,14*sqrt{50/29000}=

$$\frac { 144 } { 3,5 \times 3,14 } \times \sqrt { \frac { 50 } { 29000 } } =$$

Evaluate

$$\frac{1440\sqrt{145}}{31871}\approx 0.544065018$$

Solution Steps

Multiply 3,5 and 3,14 to get 10,99.

$$\frac{144}{10,99}\sqrt{\frac{50}{29000}}$$

Expand \frac{144}{10,99} by multiplying both numerator and the denominator by 100.

$$\frac{14400}{1099}\sqrt{\frac{50}{29000}}$$

Reduce the fraction \frac{50}{29000} to lowest terms by extracting and canceling out 50.

$$\frac{14400}{1099}\sqrt{\frac{1}{580}}$$

Rewrite the square root of the division \sqrt{\frac{1}{580}} as the division of square roots \frac{\sqrt{1}}{\sqrt{580}}.

$$\frac{14400}{1099}\times \frac{\sqrt{1}}{\sqrt{580}}$$

Calculate the square root of 1 and get 1.

$$\frac{14400}{1099}\times \frac{1}{\sqrt{580}}$$

Factor 580=2^{2}\times 145. Rewrite the square root of the product \sqrt{2^{2}\times 145} as the product of square roots \sqrt{2^{2}}\sqrt{145}. Take the square root of 2^{2}.

$$\frac{14400}{1099}\times \frac{1}{2\sqrt{145}}$$

Rationalize the denominator of \frac{1}{2\sqrt{145}} by multiplying numerator and denominator by \sqrt{145}.

$$\frac{14400}{1099}\times \frac{\sqrt{145}}{2\left(\sqrt{145}\right)^{2}}$$

The square of \sqrt{145} is 145.

$$\frac{14400}{1099}\times \frac{\sqrt{145}}{2\times 145}$$

Multiply 2 and 145 to get 290.

$$\frac{14400}{1099}\times \frac{\sqrt{145}}{290}$$

Multiply \frac{14400}{1099} times \frac{\sqrt{145}}{290} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14400\sqrt{145}}{1099\times 290}$$

Cancel out 10 in both numerator and denominator.

$$\frac{1440\sqrt{145}}{29\times 1099}$$

Multiply 29 and 1099 to get 31871.

$$\frac{1440\sqrt{145}}{31871}$$