Solve 10^9/2pisqrt{6800}

$$\frac{ { 10 }^{ 9 } }{ 2 \pi \sqrt{ 6800 } }$$

Evaluate

$$\frac{25000000\sqrt{17}}{17\pi }\approx 1930037.180020742$$

Solution Steps

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{1000000000}{2\pi \sqrt{6800}}$$

Factor 6800=20^{2}\times 17. Rewrite the square root of the product \sqrt{20^{2}\times 17} as the product of square roots \sqrt{20^{2}}\sqrt{17}. Take the square root of 20^{2}.

$$\frac{1000000000}{2\pi \times 20\sqrt{17}}$$

Multiply 2 and 20 to get 40.

$$\frac{1000000000}{40\pi \sqrt{17}}$$

Rationalize the denominator of \frac{1000000000}{40\pi \sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{1000000000\sqrt{17}}{40\pi \left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{1000000000\sqrt{17}}{40\pi \times 17}$$

Cancel out 40 in both numerator and denominator.

$$\frac{25000000\sqrt{17}}{17\pi }$$