Solve 5/51^22x25sqrt{8%539+3}

$$\frac{ 5 }{ { 51 }^{ 2 } 2x25 \sqrt{ 8 \% 539+3 } }$$

Evaluate

$$\frac{25\sqrt{1153}}{5997906x_{25}}$$

Short Solution Steps

Calculate 51 to the power of 2 and get 2601.

$$\frac{5}{2\times 2601x_{25}\sqrt{\frac{8}{100}\times 539+3}}$$

Multiply 2 and 2601 to get 5202.

$$\frac{5}{5202x_{25}\sqrt{\frac{8}{100}\times 539+3}}$$

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$\frac{5}{5202x_{25}\sqrt{\frac{2}{25}\times 539+3}}$$

Express \frac{2}{25}\times 539 as a single fraction.

$$\frac{5}{5202x_{25}\sqrt{\frac{2\times 539}{25}+3}}$$

Multiply 2 and 539 to get 1078.

$$\frac{5}{5202x_{25}\sqrt{\frac{1078}{25}+3}}$$

Convert 3 to fraction \frac{75}{25}.

$$\frac{5}{5202x_{25}\sqrt{\frac{1078}{25}+\frac{75}{25}}}$$

Since \frac{1078}{25} and \frac{75}{25} have the same denominator, add them by adding their numerators.

$$\frac{5}{5202x_{25}\sqrt{\frac{1078+75}{25}}}$$

Add 1078 and 75 to get 1153.

$$\frac{5}{5202x_{25}\sqrt{\frac{1153}{25}}}$$

Rewrite the square root of the division \sqrt{\frac{1153}{25}} as the division of square roots \frac{\sqrt{1153}}{\sqrt{25}}.

$$\frac{5}{5202x_{25}\times \frac{\sqrt{1153}}{\sqrt{25}}}$$

Calculate the square root of 25 and get 5.

$$\frac{5}{5202x_{25}\times \frac{\sqrt{1153}}{5}}$$

Express 5202\times \frac{\sqrt{1153}}{5} as a single fraction.

$$\frac{5}{\frac{5202\sqrt{1153}}{5}x_{25}}$$

Express \frac{5202\sqrt{1153}}{5}x_{25} as a single fraction.

$$\frac{5}{\frac{5202\sqrt{1153}x_{25}}{5}}$$

Divide 5 by \frac{5202\sqrt{1153}x_{25}}{5} by multiplying 5 by the reciprocal of \frac{5202\sqrt{1153}x_{25}}{5}.

$$\frac{5\times 5}{5202\sqrt{1153}x_{25}}$$

Rationalize the denominator of \frac{5\times 5}{5202\sqrt{1153}x_{25}} by multiplying numerator and denominator by \sqrt{1153}.

$$\frac{5\times 5\sqrt{1153}}{5202\left(\sqrt{1153}\right)^{2}x_{25}}$$

The square of \sqrt{1153} is 1153.

$$\frac{5\times 5\sqrt{1153}}{5202\times 1153x_{25}}$$

Multiply 5 and 5 to get 25.

$$\frac{25\sqrt{1153}}{5202\times 1153x_{25}}$$

Multiply 5202 and 1153 to get 5997906.

$$\frac{25\sqrt{1153}}{5997906x_{25}}$$

Differentiate w.r.t. x_25

$$-\frac{25\sqrt{1153}}{5997906x_{25}^{2}}$$