Solve 243*10^8div((2pidivsqrt{2})*158*6000*20)

$$243 \times { 10 }^{ 8 } \div ((2 \pi \div \sqrt{ 2 } ) \times 158 \times 6000 \times 20)$$

Evaluate

$$\frac{50625\sqrt{2}}{79\pi }\approx 288.471604465$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\frac{243\times 100000000}{20\times 158\times 6000\times \frac{2\pi }{\sqrt{2}}}$$

Multiply 243 and 100000000 to get 24300000000.

$$\frac{24300000000}{20\times 158\times 6000\times \frac{2\pi }{\sqrt{2}}}$$

Multiply 20 and 158 to get 3160.

$$\frac{24300000000}{3160\times 6000\times \frac{2\pi }{\sqrt{2}}}$$

Multiply 3160 and 6000 to get 18960000.

$$\frac{24300000000}{18960000\times \frac{2\pi }{\sqrt{2}}}$$

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

$$\frac{24300000000}{18960000\times \frac{2\pi \sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{24300000000}{18960000\times \frac{2\pi \sqrt{2}}{2}}$$

Cancel out 2, the greatest common factor in 18960000 and 2.

$$\frac{24300000000}{9480000\times 2\pi \sqrt{2}}$$

Rationalize the denominator of \frac{24300000000}{9480000\times 2\pi \sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{24300000000\sqrt{2}}{9480000\times 2\pi \left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{24300000000\sqrt{2}}{9480000\times 2\pi \times 2}$$

Cancel out 2\times 2\times 120000 in both numerator and denominator.

$$\frac{50625\sqrt{2}}{79\pi }$$