Solve 31536000/sqrt{1-{left(frac{27000{300000}right)}^2}}

$$\frac{ 31536000 }{ \sqrt{ 1- { \left( \frac{ 27000 }{ 300000 } \right) }^{ 2 } } }$$

Evaluate

$$\frac{3153600000\sqrt{9919}}{9919}\approx 31664501.978603408$$

Solution Steps

Reduce the fraction \frac{27000}{300000} to lowest terms by extracting and canceling out 3000.

$$\frac{31536000}{\sqrt{1-\left(\frac{9}{100}\right)^{2}}}$$

Calculate \frac{9}{100} to the power of 2 and get \frac{81}{10000}.

$$\frac{31536000}{\sqrt{1-\frac{81}{10000}}}$$

Subtract \frac{81}{10000} from 1 to get \frac{9919}{10000}.

$$\frac{31536000}{\sqrt{\frac{9919}{10000}}}$$

Rewrite the square root of the division \sqrt{\frac{9919}{10000}} as the division of square roots \frac{\sqrt{9919}}{\sqrt{10000}}.

$$\frac{31536000}{\frac{\sqrt{9919}}{\sqrt{10000}}}$$

Calculate the square root of 10000 and get 100.

$$\frac{31536000}{\frac{\sqrt{9919}}{100}}$$

Divide 31536000 by \frac{\sqrt{9919}}{100} by multiplying 31536000 by the reciprocal of \frac{\sqrt{9919}}{100}.

$$\frac{31536000\times 100}{\sqrt{9919}}$$

Rationalize the denominator of \frac{31536000\times 100}{\sqrt{9919}} by multiplying numerator and denominator by \sqrt{9919}.

$$\frac{31536000\times 100\sqrt{9919}}{\left(\sqrt{9919}\right)^{2}}$$

The square of \sqrt{9919} is 9919.

$$\frac{31536000\times 100\sqrt{9919}}{9919}$$

Multiply 31536000 and 100 to get 3153600000.

$$\frac{3153600000\sqrt{9919}}{9919}$$