Solve 840*10^8div((2pidivsqrt{2})*10.5*6000*20)

$$840 \times { 10 }^{ 8 } \div ((2 \pi \div \sqrt{ 2 } ) \times 10.5 \times 6000 \times 20)$$

Evaluate

$$\frac{100000\sqrt{2}}{3\pi }\approx 15005.271935952$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\frac{840\times 100000000}{10.5\times 20\times 6000\times \frac{2\pi }{\sqrt{2}}}$$

Multiply 840 and 100000000 to get 84000000000.

$$\frac{84000000000}{10.5\times 20\times 6000\times \frac{2\pi }{\sqrt{2}}}$$

Multiply 10.5 and 20 to get 210.

$$\frac{84000000000}{210\times 6000\times \frac{2\pi }{\sqrt{2}}}$$

Multiply 210 and 6000 to get 1260000.

$$\frac{84000000000}{1260000\times \frac{2\pi }{\sqrt{2}}}$$

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

$$\frac{84000000000}{1260000\times \frac{2\pi \sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{84000000000}{1260000\times \frac{2\pi \sqrt{2}}{2}}$$

Cancel out 2, the greatest common factor in 1260000 and 2.

$$\frac{84000000000}{630000\times 2\pi \sqrt{2}}$$

Rationalize the denominator of \frac{84000000000}{630000\times 2\pi \sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{84000000000\sqrt{2}}{630000\times 2\pi \left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{84000000000\sqrt{2}}{630000\times 2\pi \times 2}$$

Cancel out 2\times 2\times 210000 in both numerator and denominator.

$$\frac{100000\sqrt{2}}{3\pi }$$