Solve 366^2*frac{4/sqrt{3}}{2*200*pi*12*12}

$$\frac{ { 366 }^{ 2 } \times \frac{ 4 }{ \sqrt{ 3 } } }{ 2 \times 200 \times \pi \times 12 \times 12 }$$

Evaluate

$$\frac{3721\sqrt{3}}{1200\pi }\approx 1.709579017$$

Solution Steps

Calculate 366 to the power of 2 and get 133956.

$$\frac{133956\times \frac{4}{\sqrt{3}}}{2\times 200\pi \times 12\times 12}$$

Rationalize the denominator of \frac{4}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{133956\times \frac{4\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{2\times 200\pi \times 12\times 12}$$

The square of \sqrt{3} is 3.

$$\frac{133956\times \frac{4\sqrt{3}}{3}}{2\times 200\pi \times 12\times 12}$$

Cancel out 3, the greatest common factor in 133956 and 3.

$$\frac{44652\times 4\sqrt{3}}{2\times 200\pi \times 12\times 12}$$

Multiply 2 and 200 to get 400.

$$\frac{44652\times 4\sqrt{3}}{400\pi \times 12\times 12}$$

Multiply 400 and 12 to get 4800.

$$\frac{44652\times 4\sqrt{3}}{4800\pi \times 12}$$

Multiply 4800 and 12 to get 57600.

$$\frac{44652\times 4\sqrt{3}}{57600\pi }$$

Cancel out 4\times 12 in both numerator and denominator.

$$\frac{3721\sqrt{3}}{1200\pi }$$