Solve 8/sqrt{2*314*900}

$$\frac{ 8 }{ \sqrt{ 2 \times 314 \times 900 } }$$

Evaluate

$$\frac{2\sqrt{157}}{2355}\approx 0.010641158$$

Solution Steps

Multiply 2 and 314 to get 628.

$$\frac{8}{\sqrt{628\times 900}}$$

Multiply 628 and 900 to get 565200.

$$\frac{8}{\sqrt{565200}}$$

Factor 565200=60^{2}\times 157. Rewrite the square root of the product \sqrt{60^{2}\times 157} as the product of square roots \sqrt{60^{2}}\sqrt{157}. Take the square root of 60^{2}.

$$\frac{8}{60\sqrt{157}}$$

Rationalize the denominator of \frac{8}{60\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{8\sqrt{157}}{60\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{8\sqrt{157}}{60\times 157}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2\sqrt{157}}{15\times 157}$$

Multiply 15 and 157 to get 2355.

$$\frac{2\sqrt{157}}{2355}$$