Solve 245465225255552258889562522525253/99982555529*455sqrt{52}

$$\frac{ 245465225255552258889562522525253 }{ 99982555529 \times 455 \sqrt{ 52 } }$$

Evaluate

$$\frac{245465225255552258889562522525253\sqrt{13}}{1182793631908070}\approx 7.482602477 \cdot 10^{17}$$

Solution Steps

Multiply 455 and 99982555529 to get 45492062765695.

$$\frac{245465225255552258889562522525253}{45492062765695\sqrt{52}}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$\frac{245465225255552258889562522525253}{45492062765695\times 2\sqrt{13}}$$

Multiply 45492062765695 and 2 to get 90984125531390.

$$\frac{245465225255552258889562522525253}{90984125531390\sqrt{13}}$$

Rationalize the denominator of \frac{245465225255552258889562522525253}{90984125531390\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{245465225255552258889562522525253\sqrt{13}}{90984125531390\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{245465225255552258889562522525253\sqrt{13}}{90984125531390\times 13}$$

Multiply 90984125531390 and 13 to get 1182793631908070.

$$\frac{245465225255552258889562522525253\sqrt{13}}{1182793631908070}$$