Solve 8/sqrt{2*3.14*900}

$$\frac{ 8 }{ \sqrt{ 2 \times 3.14 \times 900 } }$$

Evaluate

$$\frac{4\sqrt{157}}{471}\approx 0.106411585$$

Solution Steps

Multiply 2 and 3.14 to get 6.28.

$$\frac{8}{\sqrt{6.28\times 900}}$$

Multiply 6.28 and 900 to get 5652.

$$\frac{8}{\sqrt{5652}}$$

Factor 5652=6^{2}\times 157. Rewrite the square root of the product \sqrt{6^{2}\times 157} as the product of square roots \sqrt{6^{2}}\sqrt{157}. Take the square root of 6^{2}.

$$\frac{8}{6\sqrt{157}}$$

Rationalize the denominator of \frac{8}{6\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{8\sqrt{157}}{6\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{8\sqrt{157}}{6\times 157}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4\sqrt{157}}{3\times 157}$$

Multiply 3 and 157 to get 471.

$$\frac{4\sqrt{157}}{471}$$