Solve 533(2)/512(2718)(sqrt{2*314)}

$$\frac{ 533(2) }{ 512(2718)( \sqrt{ 2 \times 314) } }$$

Evaluate

$$\frac{533\sqrt{157}}{218483712}\approx 0.000030567$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{533}{256\times 2718\sqrt{2\times 314}}$$

Multiply 256 and 2718 to get 695808.

$$\frac{533}{695808\sqrt{2\times 314}}$$

Multiply 2 and 314 to get 628.

$$\frac{533}{695808\sqrt{628}}$$

Factor 628=2^{2}\times 157. Rewrite the square root of the product \sqrt{2^{2}\times 157} as the product of square roots \sqrt{2^{2}}\sqrt{157}. Take the square root of 2^{2}.

$$\frac{533}{695808\times 2\sqrt{157}}$$

Multiply 695808 and 2 to get 1391616.

$$\frac{533}{1391616\sqrt{157}}$$

Rationalize the denominator of \frac{533}{1391616\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{533\sqrt{157}}{1391616\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{533\sqrt{157}}{1391616\times 157}$$

Multiply 1391616 and 157 to get 218483712.

$$\frac{533\sqrt{157}}{218483712}$$