Solve 1200*10^8div((2pidivsqrt{2})*5.25*6000*20)

$$1200 \times { 10 }^{ 8 } \div ((2 \pi \div \sqrt{ 2 } ) \times 5.25 \times 6000 \times 20)$$

Evaluate

$$\frac{2000000\sqrt{2}}{21\pi }\approx 42872.205531291$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\frac{1200\times 100000000}{5.25\times 20\times 6000\times \frac{2\pi }{\sqrt{2}}}$$

Multiply 1200 and 100000000 to get 120000000000.

$$\frac{120000000000}{5.25\times 20\times 6000\times \frac{2\pi }{\sqrt{2}}}$$

Multiply 5.25 and 20 to get 105.

$$\frac{120000000000}{105\times 6000\times \frac{2\pi }{\sqrt{2}}}$$

Multiply 105 and 6000 to get 630000.

$$\frac{120000000000}{630000\times \frac{2\pi }{\sqrt{2}}}$$

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

$$\frac{120000000000}{630000\times \frac{2\pi \sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{120000000000}{630000\times \frac{2\pi \sqrt{2}}{2}}$$

Cancel out 2, the greatest common factor in 630000 and 2.

$$\frac{120000000000}{315000\times 2\pi \sqrt{2}}$$

Rationalize the denominator of \frac{120000000000}{315000\times 2\pi \sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{120000000000\sqrt{2}}{315000\times 2\pi \left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{120000000000\sqrt{2}}{315000\times 2\pi \times 2}$$

Cancel out 2\times 2\times 15000 in both numerator and denominator.

$$\frac{2000000\sqrt{2}}{21\pi }$$