Solve 6*6710^-11300*250/0.02*2sqrt{2/2}=

$$\frac{ 6 \cdot 67 { 10 }^{ -11 } 300 \cdot 250 }{ 0.02 \cdot 2 \frac{ \sqrt{ 2 } }{ 2 } } =$$

Evaluate

$$\frac{603\sqrt{2}}{80000}\approx 0.010659635$$

Solution Steps

Multiply 6 and 67 to get 402.

$$\frac{402\times 10^{-11}\times 300\times 250}{0.02\times 2\times \frac{\sqrt{2}}{2}}$$

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\frac{402\times \frac{1}{100000000000}\times 300\times 250}{0.02\times 2\times \frac{\sqrt{2}}{2}}$$

Multiply 402 and \frac{1}{100000000000} to get \frac{201}{50000000000}.

$$\frac{\frac{201}{50000000000}\times 300\times 250}{0.02\times 2\times \frac{\sqrt{2}}{2}}$$

Multiply \frac{201}{50000000000} and 300 to get \frac{603}{500000000}.

$$\frac{\frac{603}{500000000}\times 250}{0.02\times 2\times \frac{\sqrt{2}}{2}}$$

Multiply \frac{603}{500000000} and 250 to get \frac{603}{2000000}.

$$\frac{\frac{603}{2000000}}{0.02\times 2\times \frac{\sqrt{2}}{2}}$$

Multiply 0.02 and 2 to get 0.04.

$$\frac{\frac{603}{2000000}}{0.04\times \frac{\sqrt{2}}{2}}$$

Express \frac{\frac{603}{2000000}}{0.04\times \frac{\sqrt{2}}{2}} as a single fraction.

$$\frac{603}{2000000\times 0.04\times \frac{\sqrt{2}}{2}}$$

Multiply 2000000 and 0.04 to get 80000.

$$\frac{603}{80000\times \frac{\sqrt{2}}{2}}$$

Cancel out 2, the greatest common factor in 80000 and 2.

$$\frac{603}{40000\sqrt{2}}$$

Rationalize the denominator of \frac{603}{40000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{603\sqrt{2}}{40000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{603\sqrt{2}}{40000\times 2}$$

Multiply 40000 and 2 to get 80000.

$$\frac{603\sqrt{2}}{80000}$$