Solve 1/145sqrt{138354362*1/frac{5.44{521+4}}}

$$\frac{ 1 }{ 14 } 5 \sqrt{ 138354362 \times \frac{ 1 }{ \frac{ 5.44 }{ 521+4 } } }$$

Evaluate

$$\frac{125\sqrt{24696253617}}{476}\approx 41268.491904133$$

Solution Steps

Multiply 5 and \frac{1}{14} to get \frac{5}{14}.

$$\frac{5}{14}\sqrt{138354362\times \frac{1}{\frac{5.44}{521+4}}}$$

Divide 1 by \frac{5.44}{521+4} by multiplying 1 by the reciprocal of \frac{5.44}{521+4}.

$$\frac{5}{14}\sqrt{138354362\times \frac{521+4}{5.44}}$$

Add 521 and 4 to get 525.

$$\frac{5}{14}\sqrt{138354362\times \frac{525}{5.44}}$$

Expand \frac{525}{5.44} by multiplying both numerator and the denominator by 100.

$$\frac{5}{14}\sqrt{138354362\times \frac{52500}{544}}$$

Reduce the fraction \frac{52500}{544} to lowest terms by extracting and canceling out 4.

$$\frac{5}{14}\sqrt{138354362\times \frac{13125}{136}}$$

Express 138354362\times \frac{13125}{136} as a single fraction.

$$\frac{5}{14}\sqrt{\frac{138354362\times 13125}{136}}$$

Multiply 138354362 and 13125 to get 1815901001250.

$$\frac{5}{14}\sqrt{\frac{1815901001250}{136}}$$

Reduce the fraction \frac{1815901001250}{136} to lowest terms by extracting and canceling out 2.

$$\frac{5}{14}\sqrt{\frac{907950500625}{68}}$$

Rewrite the square root of the division \sqrt{\frac{907950500625}{68}} as the division of square roots \frac{\sqrt{907950500625}}{\sqrt{68}}.

$$\frac{5}{14}\times \frac{\sqrt{907950500625}}{\sqrt{68}}$$

Factor 907950500625=25^{2}\times 1452720801. Rewrite the square root of the product \sqrt{25^{2}\times 1452720801} as the product of square roots \sqrt{25^{2}}\sqrt{1452720801}. Take the square root of 25^{2}.

$$\frac{5}{14}\times \frac{25\sqrt{1452720801}}{\sqrt{68}}$$

Factor 68=2^{2}\times 17. Rewrite the square root of the product \sqrt{2^{2}\times 17} as the product of square roots \sqrt{2^{2}}\sqrt{17}. Take the square root of 2^{2}.

$$\frac{5}{14}\times \frac{25\sqrt{1452720801}}{2\sqrt{17}}$$

Rationalize the denominator of \frac{25\sqrt{1452720801}}{2\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{5}{14}\times \frac{25\sqrt{1452720801}\sqrt{17}}{2\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{5}{14}\times \frac{25\sqrt{1452720801}\sqrt{17}}{2\times 17}$$

To multiply \sqrt{1452720801} and \sqrt{17}, multiply the numbers under the square root.

$$\frac{5}{14}\times \frac{25\sqrt{24696253617}}{2\times 17}$$

Multiply 2 and 17 to get 34.

$$\frac{5}{14}\times \frac{25\sqrt{24696253617}}{34}$$

Multiply \frac{5}{14} times \frac{25\sqrt{24696253617}}{34} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 25\sqrt{24696253617}}{14\times 34}$$

Multiply 5 and 25 to get 125.

$$\frac{125\sqrt{24696253617}}{14\times 34}$$

Multiply 14 and 34 to get 476.

$$\frac{125\sqrt{24696253617}}{476}$$