Solve 3002/sqrt{13}*0.1+200*0.31/sqrt{5}

$$300 \frac{ 2 }{ \sqrt{ 13 } } \times 0.1+200 \cdot 0.3 \frac{ 1 }{ \sqrt{ 5 } }$$

Evaluate

$$\frac{60\sqrt{13}+156\sqrt{5}}{13}\approx 43.473821617$$

Short Solution Steps

Multiply 0.1 and 300 to get 30.

$$30\times \frac{2}{\sqrt{13}}+0.3\times 200\times \frac{1}{\sqrt{5}}$$

Rationalize the denominator of \frac{2}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$30\times \frac{2\sqrt{13}}{\left(\sqrt{13}\right)^{2}}+0.3\times 200\times \frac{1}{\sqrt{5}}$$

The square of \sqrt{13} is 13.

$$30\times \frac{2\sqrt{13}}{13}+0.3\times 200\times \frac{1}{\sqrt{5}}$$

Express 30\times \frac{2\sqrt{13}}{13} as a single fraction.

$$\frac{30\times 2\sqrt{13}}{13}+0.3\times 200\times \frac{1}{\sqrt{5}}$$

Multiply 0.3 and 200 to get 60.

$$\frac{30\times 2\sqrt{13}}{13}+60\times \frac{1}{\sqrt{5}}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{30\times 2\sqrt{13}}{13}+60\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{30\times 2\sqrt{13}}{13}+60\times \frac{\sqrt{5}}{5}$$

Cancel out 5, the greatest common factor in 60 and 5.

$$\frac{30\times 2\sqrt{13}}{13}+12\sqrt{5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12\sqrt{5} times \frac{13}{13}.

$$\frac{30\times 2\sqrt{13}}{13}+\frac{13\times 12\sqrt{5}}{13}$$

Since \frac{30\times 2\sqrt{13}}{13} and \frac{13\times 12\sqrt{5}}{13} have the same denominator, add them by adding their numerators.

$$\frac{30\times 2\sqrt{13}+13\times 12\sqrt{5}}{13}$$

Do the multiplications in 30\times 2\sqrt{13}+13\times 12\sqrt{5}.

$$\frac{60\sqrt{13}+156\sqrt{5}}{13}$$

Factor

$$\frac{12 \sqrt{5} \sqrt{13} {(\sqrt{5} + \sqrt{13})}}{13} = 43.47382161675436$$