Solve 120+1.6912120!/sqrt{50}

$$120+1.6912 \frac{ 120 ! }{ \sqrt{ 50 } }$$

Evaluate

$$1131328732722516367979302525307763811871624459860303601517203939101252267201268140761725758830798100038835619720500366994244619180640701568946031126065577609008794123354977075200000000000000000000000\sqrt{2}+120\approx 1.599940437 \cdot 10^{198}$$

Solution Steps

The factorial of 120 is 6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000.

$$120+1.6912\times \frac{6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000}{\sqrt{50}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$120+1.6912\times \frac{6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000}{5\sqrt{2}}$$

Rationalize the denominator of \frac{6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$120+1.6912\times \frac{6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$120+1.6912\times \frac{6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000\sqrt{2}}{5\times 2}$$

Cancel out 2\times 5 in both numerator and denominator.

$$120+1.6912\times 668950291344912705758811805409037258675274633313802981029567135230163355724496298936687416527198498130815763789321409055253440858940812185989848111438965000596496052125696000000000000000000000000000\sqrt{2}$$

Multiply 1.6912 and 668950291344912705758811805409037258675274633313802981029567135230163355724496298936687416527198498130815763789321409055253440858940812185989848111438965000596496052125696000000000000000000000000000 to get 1131328732722516367979302525307763811871624459860303601517203939101252267201268140761725758830798100038835619720500366994244619180640701568946031126065577609008794123354977075200000000000000000000000.

$$120+1131328732722516367979302525307763811871624459860303601517203939101252267201268140761725758830798100038835619720500366994244619180640701568946031126065577609008794123354977075200000000000000000000000\sqrt{2}$$