Solve 28.4*0.0455^2*0.2*0.101325+0.2/273.15+13.8*sqrt{0.2/0.7*9.81}

$$28.4 \times { 0.0455 }^{ 2 } \times 0.2 \times \frac{ 0.101325+0.2 }{ 273.15+13.8 } \times \sqrt{ \frac{ 0.2 }{ 0.7 \times 9.81 } }$$

Evaluate

$$\frac{1012367629\sqrt{1526}}{18766530000000000}\approx 0.000002107$$

Solution Steps

Multiply 0.2 and 28.4 to get 5.68.

$$5.68\times 0.0455^{2}\times \frac{0.101325+0.2}{273.15+13.8}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Calculate 0.0455 to the power of 2 and get 0.00207025.

$$5.68\times 0.00207025\times \frac{0.101325+0.2}{273.15+13.8}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Multiply 5.68 and 0.00207025 to get 0.01175902.

$$0.01175902\times \frac{0.101325+0.2}{273.15+13.8}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Add 0.101325 and 0.2 to get 0.301325.

$$0.01175902\times \frac{0.301325}{273.15+13.8}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Add 273.15 and 13.8 to get 286.95.

$$0.01175902\times \frac{0.301325}{286.95}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Expand \frac{0.301325}{286.95} by multiplying both numerator and the denominator by 1000000.

$$0.01175902\times \frac{301325}{286950000}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Reduce the fraction \frac{301325}{286950000} to lowest terms by extracting and canceling out 25.

$$0.01175902\times \frac{12053}{11478000}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Convert decimal number 0.01175902 to fraction \frac{1175902}{100000000}. Reduce the fraction \frac{1175902}{100000000} to lowest terms by extracting and canceling out 2.

$$\frac{587951}{50000000}\times \frac{12053}{11478000}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Multiply \frac{587951}{50000000} times \frac{12053}{11478000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{587951\times 12053}{50000000\times 11478000}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Do the multiplications in the fraction \frac{587951\times 12053}{50000000\times 11478000}.

$$\frac{7086573403}{573900000000000}\sqrt{\frac{0.2}{0.7\times 9.81}}$$

Multiply 0.7 and 9.81 to get 6.867.

$$\frac{7086573403}{573900000000000}\sqrt{\frac{0.2}{6.867}}$$

Expand \frac{0.2}{6.867} by multiplying both numerator and the denominator by 1000.

$$\frac{7086573403}{573900000000000}\sqrt{\frac{200}{6867}}$$

Rewrite the square root of the division \sqrt{\frac{200}{6867}} as the division of square roots \frac{\sqrt{200}}{\sqrt{6867}}.

$$\frac{7086573403}{573900000000000}\times \frac{\sqrt{200}}{\sqrt{6867}}$$

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

$$\frac{7086573403}{573900000000000}\times \frac{10\sqrt{2}}{\sqrt{6867}}$$

Factor 6867=3^{2}\times 763. Rewrite the square root of the product \sqrt{3^{2}\times 763} as the product of square roots \sqrt{3^{2}}\sqrt{763}. Take the square root of 3^{2}.

$$\frac{7086573403}{573900000000000}\times \frac{10\sqrt{2}}{3\sqrt{763}}$$

Rationalize the denominator of \frac{10\sqrt{2}}{3\sqrt{763}} by multiplying numerator and denominator by \sqrt{763}.

$$\frac{7086573403}{573900000000000}\times \frac{10\sqrt{2}\sqrt{763}}{3\left(\sqrt{763}\right)^{2}}$$

The square of \sqrt{763} is 763.

$$\frac{7086573403}{573900000000000}\times \frac{10\sqrt{2}\sqrt{763}}{3\times 763}$$

To multiply \sqrt{2} and \sqrt{763}, multiply the numbers under the square root.

$$\frac{7086573403}{573900000000000}\times \frac{10\sqrt{1526}}{3\times 763}$$

Multiply 3 and 763 to get 2289.

$$\frac{7086573403}{573900000000000}\times \frac{10\sqrt{1526}}{2289}$$

Multiply \frac{7086573403}{573900000000000} times \frac{10\sqrt{1526}}{2289} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7086573403\times 10\sqrt{1526}}{573900000000000\times 2289}$$

Cancel out 7\times 10 in both numerator and denominator.

$$\frac{1012367629\sqrt{1526}}{327\times 57390000000000}$$

Multiply 327 and 57390000000000 to get 18766530000000000.

$$\frac{1012367629\sqrt{1526}}{18766530000000000}$$