Solve sqrt{1/2^4-1}*89916

$$\sqrt{ \frac{ 1 }{ { 2 }^{ 4 } -1 } } \times 89916$$

Evaluate

$$\frac{29972\sqrt{15}}{5}\approx 23216.211370506$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$89916\sqrt{\frac{1}{16-1}}$$

Subtract 1 from 16 to get 15.

$$89916\sqrt{\frac{1}{15}}$$

Rewrite the square root of the division \sqrt{\frac{1}{15}} as the division of square roots \frac{\sqrt{1}}{\sqrt{15}}.

$$89916\times \frac{\sqrt{1}}{\sqrt{15}}$$

Calculate the square root of 1 and get 1.

$$89916\times \frac{1}{\sqrt{15}}$$

Rationalize the denominator of \frac{1}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$89916\times \frac{\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$89916\times \frac{\sqrt{15}}{15}$$

Express 89916\times \frac{\sqrt{15}}{15} as a single fraction.

$$\frac{89916\sqrt{15}}{15}$$

Divide 89916\sqrt{15} by 15 to get \frac{29972}{5}\sqrt{15}.

$$\frac{29972}{5}\sqrt{15}$$