Solve frac{sqrt{8}}{9801}4!*left(1103+26390right)/396^4

$$\frac{ \sqrt{ 8 } }{ 9801 } \frac{ 4 ! \times \left( 1103+26390 \right) }{ { 396 }^{ 4 } }$$

Evaluate

$$\frac{27493\sqrt{2}}{5021227463472}\approx 7.743320484 \cdot 10^{-9}$$

Solution Steps

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

$$\frac{2\sqrt{2}}{9801}\times \frac{4!\left(1103+26390\right)}{396^{4}}$$

The factorial of 4 is 24.

$$\frac{2\sqrt{2}}{9801}\times \frac{24\left(1103+26390\right)}{396^{4}}$$

Add 1103 and 26390 to get 27493.

$$\frac{2\sqrt{2}}{9801}\times \frac{24\times 27493}{396^{4}}$$

Multiply 24 and 27493 to get 659832.

$$\frac{2\sqrt{2}}{9801}\times \frac{659832}{396^{4}}$$

Calculate 396 to the power of 4 and get 24591257856.

$$\frac{2\sqrt{2}}{9801}\times \frac{659832}{24591257856}$$

Reduce the fraction \frac{659832}{24591257856} to lowest terms by extracting and canceling out 24.

$$\frac{2\sqrt{2}}{9801}\times \frac{27493}{1024635744}$$

Multiply \frac{2\sqrt{2}}{9801} times \frac{27493}{1024635744} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\sqrt{2}\times 27493}{9801\times 1024635744}$$

Cancel out 2 in both numerator and denominator.

$$\frac{27493\sqrt{2}}{9801\times 512317872}$$

Multiply 9801 and 512317872 to get 5021227463472.

$$\frac{27493\sqrt{2}}{5021227463472}$$