Solve 16^4sqrt{10.000/sqrt{25^2}}

$${ 16 }^{ 4 } \sqrt{ \frac{ 10.000 }{ \sqrt{ { 25 }^{ 2 } } } }$$

Evaluate

$$\frac{65536\sqrt{10}}{5}\approx 41448.605747359$$

Solution Steps

Calculate 16 to the power of 4 and get 65536.

$$65536\sqrt{\frac{10}{\sqrt{25^{2}}}}$$

Calculate 25 to the power of 2 and get 625.

$$65536\sqrt{\frac{10}{\sqrt{625}}}$$

Calculate the square root of 625 and get 25.

$$65536\sqrt{\frac{10}{25}}$$

Reduce the fraction \frac{10}{25} to lowest terms by extracting and canceling out 5.

$$65536\sqrt{\frac{2}{5}}$$

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

$$65536\times \frac{\sqrt{2}}{\sqrt{5}}$$

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

$$65536\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$65536\times \frac{\sqrt{2}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$65536\times \frac{\sqrt{10}}{5}$$

Express 65536\times \frac{\sqrt{10}}{5} as a single fraction.

$$\frac{65536\sqrt{10}}{5}$$