Solve frac{sqrt{left(2*3.14*100right)^2left(200*10right)^2+488^2}}{left(2*3.14*100right)^2200*10*488}

$$\frac{ \sqrt{ { \left(2 \times 3.14 \times 100 \right) }^{ 2 } { \left(200 \times 10 \right) }^{ 2 } + { 488 }^{ 2 } } }{ { \left(2 \times 3.14 \times 100 \right) }^{ 2 } 200 \times 10 \times 488 }$$

Evaluate

$$\frac{\sqrt{24649003721}}{48114848000}\approx 0.000003263$$

Solution Steps

Multiply 2 and 3.14 to get 6.28.

$$\frac{\sqrt{\left(6.28\times 100\right)^{2}\times \left(200\times 10\right)^{2}+488^{2}}}{\left(2\times 3.14\times 100\right)^{2}\times 200\times 10\times 488}$$

Multiply 6.28 and 100 to get 628.

$$\frac{\sqrt{628^{2}\times \left(200\times 10\right)^{2}+488^{2}}}{\left(2\times 3.14\times 100\right)^{2}\times 200\times 10\times 488}$$

Calculate 628 to the power of 2 and get 394384.

$$\frac{\sqrt{394384\times \left(200\times 10\right)^{2}+488^{2}}}{\left(2\times 3.14\times 100\right)^{2}\times 200\times 10\times 488}$$

Multiply 200 and 10 to get 2000.

$$\frac{\sqrt{394384\times 2000^{2}+488^{2}}}{\left(2\times 3.14\times 100\right)^{2}\times 200\times 10\times 488}$$

Calculate 2000 to the power of 2 and get 4000000.

$$\frac{\sqrt{394384\times 4000000+488^{2}}}{\left(2\times 3.14\times 100\right)^{2}\times 200\times 10\times 488}$$

Multiply 394384 and 4000000 to get 1577536000000.

$$\frac{\sqrt{1577536000000+488^{2}}}{\left(2\times 3.14\times 100\right)^{2}\times 200\times 10\times 488}$$

Calculate 488 to the power of 2 and get 238144.

$$\frac{\sqrt{1577536000000+238144}}{\left(2\times 3.14\times 100\right)^{2}\times 200\times 10\times 488}$$

Add 1577536000000 and 238144 to get 1577536238144.

$$\frac{\sqrt{1577536238144}}{\left(2\times 3.14\times 100\right)^{2}\times 200\times 10\times 488}$$

Factor 1577536238144=8^{2}\times 24649003721. Rewrite the square root of the product \sqrt{8^{2}\times 24649003721} as the product of square roots \sqrt{8^{2}}\sqrt{24649003721}. Take the square root of 8^{2}.

$$\frac{8\sqrt{24649003721}}{\left(2\times 3.14\times 100\right)^{2}\times 200\times 10\times 488}$$

Multiply 2 and 3.14 to get 6.28.

$$\frac{8\sqrt{24649003721}}{\left(6.28\times 100\right)^{2}\times 200\times 10\times 488}$$

Multiply 6.28 and 100 to get 628.

$$\frac{8\sqrt{24649003721}}{628^{2}\times 200\times 10\times 488}$$

Calculate 628 to the power of 2 and get 394384.

$$\frac{8\sqrt{24649003721}}{394384\times 200\times 10\times 488}$$

Multiply 394384 and 200 to get 78876800.

$$\frac{8\sqrt{24649003721}}{78876800\times 10\times 488}$$

Multiply 78876800 and 10 to get 788768000.

$$\frac{8\sqrt{24649003721}}{788768000\times 488}$$

Multiply 788768000 and 488 to get 384918784000.

$$\frac{8\sqrt{24649003721}}{384918784000}$$

Divide 8\sqrt{24649003721} by 384918784000 to get \frac{1}{48114848000}\sqrt{24649003721}.

$$\frac{1}{48114848000}\sqrt{24649003721}$$