Solve 52/25/412sqrt{57}

$$\frac{ \frac{ 52 }{ 25 } }{ 412 \sqrt{ 57 } }$$

Evaluate

$$\frac{13\sqrt{57}}{146775}\approx 0.000668696$$

Solution Steps

Express \frac{\frac{52}{25}}{412\sqrt{57}} as a single fraction.

$$\frac{52}{25\times 412\sqrt{57}}$$

Multiply 25 and 412 to get 10300.

$$\frac{52}{10300\sqrt{57}}$$

Rationalize the denominator of \frac{52}{10300\sqrt{57}} by multiplying numerator and denominator by \sqrt{57}.

$$\frac{52\sqrt{57}}{10300\left(\sqrt{57}\right)^{2}}$$

The square of \sqrt{57} is 57.

$$\frac{52\sqrt{57}}{10300\times 57}$$

Cancel out 4 in both numerator and denominator.

$$\frac{13\sqrt{57}}{57\times 2575}$$

Multiply 57 and 2575 to get 146775.

$$\frac{13\sqrt{57}}{146775}$$