Solve 1/2pisqrt{196/14.7*4.9*4}

$$\frac{ 1 }{ 2 \pi } \sqrt{ \frac{ 196 }{ 14.7 \times 4.9 \times 4 } }$$

Evaluate

$$\frac{5\sqrt{3}}{21\pi }\approx 0.131268785$$

Solution Steps

Multiply 14.7 and 4.9 to get 72.03.

$$\frac{1}{2\pi }\sqrt{\frac{196}{72.03\times 4}}$$

Multiply 72.03 and 4 to get 288.12.

$$\frac{1}{2\pi }\sqrt{\frac{196}{288.12}}$$

Expand \frac{196}{288.12} by multiplying both numerator and the denominator by 100.

$$\frac{1}{2\pi }\sqrt{\frac{19600}{28812}}$$

Reduce the fraction \frac{19600}{28812} to lowest terms by extracting and canceling out 196.

$$\frac{1}{2\pi }\sqrt{\frac{100}{147}}$$

Rewrite the square root of the division \sqrt{\frac{100}{147}} as the division of square roots \frac{\sqrt{100}}{\sqrt{147}}.

$$\frac{1}{2\pi }\times \frac{\sqrt{100}}{\sqrt{147}}$$

Calculate the square root of 100 and get 10.

$$\frac{1}{2\pi }\times \frac{10}{\sqrt{147}}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$\frac{1}{2\pi }\times \frac{10}{7\sqrt{3}}$$

Rationalize the denominator of \frac{10}{7\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{1}{2\pi }\times \frac{10\sqrt{3}}{7\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{1}{2\pi }\times \frac{10\sqrt{3}}{7\times 3}$$

Multiply 7 and 3 to get 21.

$$\frac{1}{2\pi }\times \frac{10\sqrt{3}}{21}$$

Multiply \frac{1}{2\pi } times \frac{10\sqrt{3}}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\sqrt{3}}{2\pi \times 21}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5\sqrt{3}}{21\pi }$$