Solve 78632/65129-255^22sqrt{4.25(265*212)812^2}

$$\frac{ 78632 }{ 65129- { 255 }^{ 22 } } \sqrt{ 4.25(265 \times 212) { 812 }^{ 2 } }$$

Evaluate

$$-\frac{423000844\sqrt{85}}{10984846247025926810563669272783943593800067901603187}\approx -3.550231837 \cdot 10^{-43}$$

Solution Steps

Calculate 255 to the power of 22 and get 87878769976207414484509354182271548750400543212890625.

$$\frac{78632}{65129-87878769976207414484509354182271548750400543212890625}\sqrt{4.25\times 265\times 212\times 812^{2}}$$

Subtract 87878769976207414484509354182271548750400543212890625 from 65129 to get -87878769976207414484509354182271548750400543212825496.

$$\frac{78632}{-87878769976207414484509354182271548750400543212825496}\sqrt{4.25\times 265\times 212\times 812^{2}}$$

Reduce the fraction \frac{78632}{-87878769976207414484509354182271548750400543212825496} to lowest terms by extracting and canceling out 8.

$$-\frac{9829}{10984846247025926810563669272783943593800067901603187}\sqrt{4.25\times 265\times 212\times 812^{2}}$$

Multiply 4.25 and 265 to get 1126.25.

$$-\frac{9829}{10984846247025926810563669272783943593800067901603187}\sqrt{1126.25\times 212\times 812^{2}}$$

Multiply 1126.25 and 212 to get 238765.

$$-\frac{9829}{10984846247025926810563669272783943593800067901603187}\sqrt{238765\times 812^{2}}$$

Calculate 812 to the power of 2 and get 659344.

$$-\frac{9829}{10984846247025926810563669272783943593800067901603187}\sqrt{238765\times 659344}$$

Multiply 238765 and 659344 to get 157428270160.

$$-\frac{9829}{10984846247025926810563669272783943593800067901603187}\sqrt{157428270160}$$

Factor 157428270160=43036^{2}\times 85. Rewrite the square root of the product \sqrt{43036^{2}\times 85} as the product of square roots \sqrt{43036^{2}}\sqrt{85}. Take the square root of 43036^{2}.

$$-\frac{9829}{10984846247025926810563669272783943593800067901603187}\times 43036\sqrt{85}$$

Express -\frac{9829}{10984846247025926810563669272783943593800067901603187}\times 43036 as a single fraction.

$$\frac{-9829\times 43036}{10984846247025926810563669272783943593800067901603187}\sqrt{85}$$

Multiply -9829 and 43036 to get -423000844.

$$\frac{-423000844}{10984846247025926810563669272783943593800067901603187}\sqrt{85}$$

Fraction \frac{-423000844}{10984846247025926810563669272783943593800067901603187} can be rewritten as -\frac{423000844}{10984846247025926810563669272783943593800067901603187} by extracting the negative sign.

$$-\frac{423000844}{10984846247025926810563669272783943593800067901603187}\sqrt{85}$$