Solve 8304246164*45/344frac{4*47{sqrt{23494249}}}

$$8304246164 \times \frac{ 45 }{ 344 \frac{ 4 \times 47 }{ \sqrt{ 23494249 } } }$$

Evaluate

$$\frac{93422769345\sqrt{23494249}}{16168}\approx 28007685438.484249115$$

Solution Steps

Multiply 4 and 47 to get 188.

$$8304246164\times \frac{45}{344\times \frac{188}{\sqrt{23494249}}}$$

Rationalize the denominator of \frac{188}{\sqrt{23494249}} by multiplying numerator and denominator by \sqrt{23494249}.

$$8304246164\times \frac{45}{344\times \frac{188\sqrt{23494249}}{\left(\sqrt{23494249}\right)^{2}}}$$

The square of \sqrt{23494249} is 23494249.

$$8304246164\times \frac{45}{344\times \frac{188\sqrt{23494249}}{23494249}}$$

Express 344\times \frac{188\sqrt{23494249}}{23494249} as a single fraction.

$$8304246164\times \frac{45}{\frac{344\times 188\sqrt{23494249}}{23494249}}$$

Divide 45 by \frac{344\times 188\sqrt{23494249}}{23494249} by multiplying 45 by the reciprocal of \frac{344\times 188\sqrt{23494249}}{23494249}.

$$8304246164\times \frac{45\times 23494249}{344\times 188\sqrt{23494249}}$$

Rationalize the denominator of \frac{45\times 23494249}{344\times 188\sqrt{23494249}} by multiplying numerator and denominator by \sqrt{23494249}.

$$8304246164\times \frac{45\times 23494249\sqrt{23494249}}{344\times 188\left(\sqrt{23494249}\right)^{2}}$$

The square of \sqrt{23494249} is 23494249.

$$8304246164\times \frac{45\times 23494249\sqrt{23494249}}{344\times 188\times 23494249}$$

Multiply 45 and 23494249 to get 1057241205.

$$8304246164\times \frac{1057241205\sqrt{23494249}}{344\times 188\times 23494249}$$

Multiply 344 and 188 to get 64672.

$$8304246164\times \frac{1057241205\sqrt{23494249}}{64672\times 23494249}$$

Multiply 64672 and 23494249 to get 1519420071328.

$$8304246164\times \frac{1057241205\sqrt{23494249}}{1519420071328}$$

Divide 1057241205\sqrt{23494249} by 1519420071328 to get \frac{45}{64672}\sqrt{23494249}.

$$8304246164\times \frac{45}{64672}\sqrt{23494249}$$

Express 8304246164\times \frac{45}{64672} as a single fraction.

$$\frac{8304246164\times 45}{64672}\sqrt{23494249}$$

Multiply 8304246164 and 45 to get 373691077380.

$$\frac{373691077380}{64672}\sqrt{23494249}$$

Reduce the fraction \frac{373691077380}{64672} to lowest terms by extracting and canceling out 4.

$$\frac{93422769345}{16168}\sqrt{23494249}$$